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Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-03-12 Daan Camps, Lin Lin, Roel Van Beeumen, Chao Yang
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 801-827, March 2024. Abstract. Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest [math] in
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Partial Degeneration of Tensors SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-03-11 Matthias Christandl, Fulvio Gesmundo, Vladimir Lysikov, Vincent Steffan
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 771-800, March 2024. Abstract. Tensors are often studied by introducing preorders such as restriction and degeneration. The former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local linear maps may vary along a curve, and the resulting tensor
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Adaptive Rational Krylov Methods for Exponential Runge–Kutta Integrators SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-03-05 Kai Bergermann, Martin Stoll
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 744-770, March 2024. Abstract. We consider the solution of large stiff systems of ODEs with explicit exponential Runge–Kutta integrators. These problems arise from semidiscretized semilinear parabolic PDEs on continuous domains or on inherently discrete graph domains. A series of results reduces the requirement of computing
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nlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-29 Huan He, Ziyuan Tang, Shifan Zhao, Yousef Saad, Yuanzhe Xi
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 712-743, March 2024. Abstract. This paper develops a new class of nonlinear acceleration algorithms based on extending conjugate residual-type procedures from linear to nonlinear equations. The main algorithm has strong similarities with Anderson acceleration as well as with inexact Newton methods—depending on which variant
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An Escape Time Formulation for Subgraph Detection and Partitioning of Directed Graphs SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-26 Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola, Peter J. Mucha, Braxton Osting
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 685-711, March 2024. Abstract. We provide a rearrangement based algorithm for detection of subgraphs of k vertices with long escape times for directed or undirected networks that is not combinatorially complex to compute. Complementing other notions of densest subgraphs and graph cuts, our method is based on the mean hitting
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Randomized Joint Diagonalization of Symmetric Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-26 Haoze He, Daniel Kressner
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 661-684, March 2024. Abstract. Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing this task. RJD applies a standard eigenvalue
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Singular Value Decomposition of Dual Matrices and its Application to Traveling Wave Identification in the Brain SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-12 Tong Wei, Weiyang Ding, Yimin Wei
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 634-660, March 2024. Abstract. Matrix factorizations in dual number algebra, a hypercomplex number system, have been applied to kinematics, spatial mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves using the singular value decomposition (SVD)
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Speeding Up Krylov Subspace Methods for Computing [math] via Randomization SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-09 Alice Cortinovis, Daniel Kressner, Yuji Nakatsukasa
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 619-633, March 2024. Abstract. This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov subspace. Such compression is usually computed
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Efficient Vectors for Block Perturbed Consistent Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-08 Susana Furtado, Charles Johnson
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 601-618, March 2024. Abstract. In prioritization schemes, based on pairwise comparisons, such as the analytical hierarchy process, it is important to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose such a vector only from efficient ones. Recently, a method
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Spectrum Maximizing Products Are Not Generically Unique SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-08 Jairo Bochi, Piotr Laskawiec
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 585-600, March 2024. Abstract. It is widely believed that typical finite families of [math] matrices admit finite products that attain the joint spectral radius. This conjecture is supported by computational experiments and it naturally leads to the following question: are these spectrum maximizing products typically unique
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Perturbation and Inverse Problems of Stochastic Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-08 Joost Berkhout, Bernd Heidergott, Paul Van Dooren
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 553-584, March 2024. Abstract. It is a classical task in perturbation analysis to find norm bounds on the effect of a perturbation [math] of a stochastic matrix [math] to its stationary distribution, i.e., to the unique normalized left Perron eigenvector. A common assumption is to consider [math] to be given and to find bounds
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Five-Precision GMRES-Based Iterative Refinement SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-08 Patrick Amestoy, Alfredo Buttari, Nicholas J. Higham, Jean-Yves L’Excellent, Theo Mary, Bastien Vieublé
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 529-552, March 2024. Abstract. GMRES-based iterative refinement in three precisions (GMRES-IR3), proposed by Carson and Higham in 2018, uses a low precision LU factorization to accelerate the solution of a linear system without compromising numerical stability or robustness. GMRES-IR3 solves the update equation of iterative
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A Unifying Framework for Higher Order Derivatives of Matrix Functions SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-08 Emanuel H. Rubensson
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 504-528, March 2024. Abstract. We present a theory for general partial derivatives of matrix functions of the form [math], where [math] is a matrix path of several variables ([math]). Building on results by Mathias [SIAM J. Matrix Anal. Appl., 17 (1996), pp. 610–620] for the first order derivative, we develop a block upper triangular
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Backpropagation through Back Substitution with a Backslash SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-05 Alan Edelman, Ekin Akyürek, Yuyang Wang
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 429-449, March 2024. Abstract. We present a linear algebra formulation of backpropagation which allows the calculation of gradients by using a generically written “backslash” or Gaussian elimination on triangular systems of equations. Generally, the matrix elements are operators. This paper has three contributions: (i) it is
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Row or Column Completion of Polynomial Matrices of Given Degree SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-07 Agurtzane Amparan, Itziar Baragaña, Silvia Marcaida, Alicia Roca
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 478-503, March 2024. Abstract. We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column) completion problem of a polynomial matrix of given degree
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Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-06 Hussam Al Daas, Grey Ballard, Laura Grigori, Suraj Kumar, Kathryn Rouse
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 450-477, March 2024. Abstract. Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine how much data movement is required (under
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More on Tensors with Different Rank and Symmetric Rank SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-02-05 Yaroslav Shitov
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 419-428, March 2024. Abstract. This is a further discussion of a previous work of the author on tensors with different rank and symmetric rank. We point out several obstructions towards extending a complex number example to the real number setting and discuss several further questions raised in the literature.
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Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-30 Francesca Arrigo, Desmond J. Higham, Vanni Noferini, Ryan Wood
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 397-418, March 2024. Abstract. We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two ways to compute the associated generating function, and
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A Fast Algorithm for Computing Macaulay Null Spaces of Bivariate Polynomial Systems SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-24 Nithin Govindarajan, Raphaël Widdershoven, Shivkumar Chandrasekaran, Lieven De Lathauwer
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 368-396, March 2024. Abstract.As a crucial first step towards finding the (approximate) common roots of a (possibly overdetermined) bivariate polynomial system of equations, the problem of determining an explicit numerical basis for the right null space of the system’s Macaulay matrix is considered. If [math] denotes the total
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An Efficient Algorithm for Integer Lattice Reduction SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-24 François Charton, Kristin Lauter, Cathy Li, Mark Tygert
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 353-367, March 2024. Abstract. A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the problem of finding a set of vectors in a given lattice such
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Constraint-Satisfying Krylov Solvers for Structure-Preserving DiscretiZations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-23 James Jackaman, Scott MacLachlan
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 327-352, March 2024. Abstract. A key consideration in the development of numerical schemes for time-dependent partial differential equations (PDEs) is the ability to preserve certain properties of the continuum solution, such as associated conservation laws or other geometric structures of the solution. There is a long history
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Structure Preserving Quaternion Biconjugate Gradient Method SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-22 Tao Li, Qing-Wen Wang
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 306-326, March 2024. Abstract. This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion
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Fast Non-Hermitian Toeplitz Eigenvalue Computations, Joining Matrixless Algorithms and FDE Approximation Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-19 Manuel Bogoya, Sergei M. Grudsky, Stefano Serra-Capizzano
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 284-305, March 2024. Abstract. The present work is devoted to the eigenvalue asymptotic expansion of the Toeplitz matrix [math], whose generating function [math] is complex-valued and has a power singularity at one point. As a consequence, [math] is non-Hermitian and we know that in this setting, the eigenvalue computation is
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Generic Eigenstructures of Hermitian Pencils SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-18 Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 260-283, March 2024. Abstract. We obtain the generic complete eigenstructures of complex Hermitian [math] matrix pencils with rank at most [math] (with [math]). To do this, we prove that the set of such pencils is the union of a finite number of bundle closures, where each bundle is the set of complex Hermitian [math] pencils
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The Joint Bidiagonalization of a Matrix Pair with Inaccurate Inner Iterations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-17 Haibo Li
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 232-259, March 2024. Abstract. The joint bidiagonalization (JBD) process iteratively reduces a matrix pair [math] to two bidiagonal forms simultaneously, which can be used for computing a partial generalized singular value decomposition (GSVD) of [math]. The process has a nested inner-outer iteration structure, where the inner
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Deflation for the Off-Diagonal Block in Symmetric Saddle Point Systems SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-17 Andrei Dumitrasc, Carola Kruse, Ulrich Rüde
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 203-231, March 2024. Abstract. Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov subspace methods, which are among the most popular iterative
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Projectively and Weakly Simultaneously Diagonalizable Matrices and their Applications SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-16 Wentao Ding, Jianze Li, Shuzhong Zhang
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 167-202, March 2024. Abstract. Characterizing simultaneously diagonalizable (SD) matrices has been receiving considerable attention in recent decades due to its wide applications and its role in matrix analysis. However, the notion of SD matrices is arguably still restrictive for wider applications. In this paper, we consider
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Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-12 Patrick Amestoy, Olivier Boiteau, Alfredo Buttari, Matthieu Gerest, Fabienne Jézéquel, Jean-Yves L’Excellent, Theo Mary
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 148-166, March 2024. Abstract. Block low-rank (BLR) compression can significantly reduce the memory and time costs of parallel sparse direct solvers. In this paper, we investigate the performance of the BLR triangular solve phase, which we observe to be underwhelming when dealing with many right-hand sides (RHS). We explain
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The Spectral Decomposition of the Continuous and Discrete Linear Elasticity Operators with Sliding Boundary Conditions SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-11 Jan Modersitzki
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 134-147, March 2024. Abstract. The elastic potential is a valuable modeling tool for many applications, including medical imaging. One reason for this is that the energy and its Gâteaux derivative, the elastic operator, have strong coupling properties. Although these properties are desirable from a modeling perspective, they
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Multiway Spectral Graph Partitioning: Cut Functions, Cheeger Inequalities, and a Simple Algorithm SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-11 Lars Eldén
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 112-133, March 2024. Abstract. The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the [math] largest eigenvalues of the normalized adjacency matrix (equivalently, the [math] smallest eigenvalues of the normalized graph Laplacian) are computed. It is shown that the information
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Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent Field Iteration SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-11 Zhaojun Bai, Ding Lu
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 84-111, March 2024. Abstract. This paper concerns a class of monotone eigenvalue problems with eigenvector nonlinearities (mNEPv). The mNEPv is encountered in applications such as the computation of joint numerical radius of matrices, best rank-one approximation of third-order partial-symmetric tensors, and distance to singularity
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Structure-Preserving Doubling Algorithms That Avoid Breakdowns for Algebraic Riccati-Type Matrix Equations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-10 Tsung-Ming Huang, Yueh-Cheng Kuo, Wen-Wei Lin, Shih-Feng Shieh
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 59-83, March 2024. Abstract. Structure-preserving doubling algorithms (SDAs) are efficient algorithms for solving Riccati-type matrix equations. However, breakdowns may occur in SDAs. To remedy this drawback, in this paper, we first introduce [math]-symplectic forms ([math]-SFs), consisting of symplectic matrix pairs with a
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An Augmented Matrix-Based CJ-FEAST SVDsolver for Computing a Partial Singular Value Decomposition with the Singular Values in a Given Interval SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-03 Zhongxiao Jia, Kailiang Zhang
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 24-58, March 2024. Abstract. The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by the authors is shown to compute the left singular vector possibly much less accurately than the right singular vector and may be numerically backward unstable when a desired singular value is small. In this paper, an alternative
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XTrace: Making the Most of Every Sample in Stochastic Trace Estimation SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2024-01-03 Ethan N. Epperly, Joel A. Tropp, Robert J. Webber
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 1-23, March 2024. Abstract. The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized algorithms, XTrace and XNysTrace, for the trace estimation problem by exploiting both variance reduction and the exchangeability
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Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-12-05 Marija Dodig, Marko Stošić
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1879-1907, December 2023. Abstract. We solve the open problem of describing the possible Kronecker invariants of quasi-regular matrix pencils under bounded rank perturbations. By a quasi-regular matrix pencil we mean the full (normal) rank matrix pencil. The solution is explicit and constructive, and it is valid over arbitrary
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Sharp Majorization-Type Cluster Robust Bounds for Block Filters and Eigensolvers SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-12-05 Ming Zhou, Merico Argentati, Andrew V. Knyazev, Klaus Neymeyr
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1852-1878, December 2023. Abstract. Convergence analysis of block iterative solvers for Hermitian eigenvalue problems and closely related research on properties of matrix-based signal filters are challenging and are attracting increased attention due to their recent applications in spectral data clustering and graph-based signal
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Uniformization Stable Markov Models and Their Jordan Algebraic Structure SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-12-05 Luke Cooper, Jeremy Sumner
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1822-1851, December 2023. Abstract. We provide a characterization of the continuous-time Markov models where the Markov matrices from the model can be parameterized directly in terms of the associated rate matrices (generators). That is, each Markov matrix can be expressed as the sum of the identity matrix and a rate matrix
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Identifiability in Continuous Lyapunov Models SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-12-04 Philipp Dettling, Roser Homs, Carlos Améndola, Mathias Drton, Niels Richard Hansen
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1799-1821, December 2023. Abstract. The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a one-time cross-sectional snapshot of a multivariate dynamic process in equilibrium. The covariance matrix for the
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PinT Preconditioner for Forward-Backward Evolutionary Equations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-11-30 Shu-Lin Wu, Zhiyong Wang, Tao Zhou
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1771-1798, December 2023. Abstract. Solving the linear system [math] is often the major computational burden when a forward-backward evolutionary equation must be solved in a problem, where [math] is the so-called all-at-once matrix of the forward subproblem after space-time discretization. An efficient solver requires a good
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Stochastic Algebraic Riccati Equations Are Almost as Easy as Deterministic Ones Theoretically SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-11-10 Zhen-Chen Guo, Xin Liang
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1749-1770, December 2023. Abstract. Stochastic algebraic Riccati equations, also known as rational algebraic Riccati equations, arising in linear-quadratic optimal control for stochastic linear time-invariant systems, were considered to be not easy to solve. The state-of-the-art numerical methods mostly rely on differentiability
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Introducing the Class of SemiDoubly Stochastic Matrices: A Novel Scaling Approach for Rectangular Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-11-10 Philip A. Knight, Luce le Gorrec, Sandrine Mouysset, Daniel Ruiz
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1731-1748, December 2023. Abstract. It is easy to verify that if [math] is a doubly stochastic matrix, then both its normal equations [math] and [math] are also doubly stochastic, but the reciprocal is not true. In this paper, we introduce and analyze the complete class of nonnegative matrices whose normal equations are doubly
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Generalized Matrix Nearness Problems SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-11-10 Zihao Li, Lek-Heng Lim
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1709-1730, December 2023. Abstract. We show that the global minimum solution of [math] can be found in closed form with singular value decompositions and generalized singular value decompositions for a variety of constraints on [math] involving rank, norm, symmetry, two-sided product, and prescribed eigenvalue. This extends
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Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-11-09 Mareike Dressler, André Uschmajew, Venkat Chandrasekaran
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1693-1708, December 2023. Abstract. The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known solution via the singular value decomposition. However
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Semidefinite Relaxation Methods for Tensor Absolute Value Equations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-11-07 Anwa Zhou, Kun Liu, Jinyan Fan
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1667-1692, December 2023. Abstract. In this paper, we consider the tensor absolute value equations (TAVEs). When one tensor is row diagonal with odd order, we show that the TAVEs can be reduced to an algebraic equation; when it is row diagonal and nonsingular with even order, we prove that the TAVEs is equivalent to a polynomial
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Generalized Perron Roots and Solvability of the Absolute Value Equation SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-30 Manuel Radons, Josué Tonelli-Cueto
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1645-1666, December 2023. Abstract. Let [math] be an [math] real matrix. The piecewise linear equation system [math] is called an absolute value equation (AVE). It is well known to be equivalent to the linear complementarity problem. Unique solvability of the AVE is known to be characterized in terms of a generalized Perron
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Contour Integration for Eigenvector Nonlinearities SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-30 Rob Claes, Karl Meerbergen, Simon Telen
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1619-1644, December 2023. Abstract. Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization of these methods which leads to a contour integration
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Solving Singular Generalized Eigenvalue Problems. Part II: Projection and Augmentation SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-25 Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1589-1618, December 2023. Abstract. Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two alternative methods. The first technique is based on a projection
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Robust Recovery of Low-Rank Matrices and Low-Tubal-Rank Tensors from Noisy Ketches SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-20 Anna Ma, Dominik Stöger, Yizhe Zhu
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1566-1588, December 2023. Abstract. A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al. [Compressed sensing and robust recovery of low rank
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Block Preconditioners for the Marker-and-Cell Discretization of the Stokes–Darcy Equations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-18 Chen Greif, Yunhui He
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1540-1565, December 2023. Abstract. We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes–Darcy equations in two dimensions, discretized by the marker-and-cell finite difference method. We analyze the eigenvalue distribution of a few ideal block preconditioners
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On Characteristic Invariants of Matrix Pencils and Linear Relations SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-17 H. Gernandt, F. Martínez Pería, F. Philipp, C. Trunk
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1510-1539, December 2023. Abstract. The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic
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A Preconditioned MINRES Method for Optimal Control of Wave Equations and its Asymptotic Spectral Distribution Theory SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-10-16 Sean Hon, Jiamei Dong, Stefano Serra-Capizzano
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1477-1509, December 2023. Abstract. In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear coefficient matrices from the optimal control problem. Namely
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Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-09-25 Yann Thanwerdas, Xavier Pennec
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1447-1476, September 2023. Abstract. The set of covariance matrices equipped with the Bures–Wasserstein distance is the orbit space of the smooth, proper, and isometric action of the orthogonal group on the Euclidean space of square matrices. This construction induces a natural orbit stratification on covariance matrices, which
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Approximate Solutions of Linear Systems at a Universal Rate SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-09-25 Stefan Steinerberger
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1436-1446, September 2023. Abstract. Let [math] be invertible, [math] unknown, and [math] given. We are interested in approximate solutions: vectors [math] such that [math] is small. We prove that for all [math], there is a composition of [math] orthogonal projections onto the [math] hyperplanes generated by the rows of [math]
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An Apocalypse-Free First-Order Low-Rank Optimization Algorithm with at Most One Rank Reduction Attempt per Iteration SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-09-22 Guillaume Olikier, P.-A. Absil
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1421-1435, September 2023. Abstract. We consider the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the real determinantal variety and present a first-order algorithm designed to find a stationary point of that problem. This algorithm applies steps of a retraction-free descent method
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Coseparable Nonnegative Matrix Factorization SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-09-15 Junjun Pan, Michael K. Ng
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1393-1420, September 2023. Abstract. Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. The aim is to find a low rank approximation for nonnegative matrix [math] by a product of two nonnegative matrices [math] and [math]. In general, NMF is NP-hard to solve while it can be solved efficiently
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Randomized Low-Rank Approximation for Symmetric Indefinite Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-09-08 Yuji Nakatsukasa, Taejun Park
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1370-1392, September 2023. Abstract. The Nyström method is a popular choice for finding a low-rank approximation to a symmetric positive semidefinite matrix. The method can fail when applied to symmetric indefinite matrices for which the error can be unboundedly large. In this work, we first identify the main challenges in finding
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Randomized Block Adaptive Linear System Solvers SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-09-06 Vivak Patel, Mohammad Jahangoshahi, D. Adrian Maldonado
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1349-1369, September 2023. Abstract. Randomized linear solvers randomly compress and solve a linear system with compelling theoretical convergence rates and computational complexities. However, such solvers suffer a substantial disconnect between their theoretical rates and actual efficiency in practice. Fortunately, these solvers
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Sensitivity of Matrix Function Based Network Communicability Measures: Computational Methods and A Priori Bounds SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-08-31 Marcel Schweitzer
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1321-1348, September 2023. Abstract. When analyzing complex networks, an important task is the identification of those nodes which play a leading role for the overall communicability of the network. In the context of modifying networks (or making them robust against targeted attacks or outages), it is also relevant to know how
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A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-08-30 Peter Benner, Yuji Nakatsukasa, Carolin Penke
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1245-1270, September 2023. Abstract. We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e., pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral division such that the method can be applied recursively
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Perturbation Theory of Transfer Function Matrices SIAM J. Matrix Anal. Appl. (IF 1.5) Pub Date : 2023-08-30 Vanni Noferini, Lauri Nyman, Javier Pérez, María C. Quintana
SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 3, Page 1299-1320, September 2023. Abstract. Zeros of rational transfer function matrices [math] are the eigenvalues of associated polynomial system matrices [math] under minimality conditions. In this paper, we define a structured condition number for a simple eigenvalue [math] of a (locally) minimal polynomial system matrix [math]