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An optimal ansatz space for moving least squares approximation on spheres Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-22 Ralf Hielscher, Tim Pöschl
We revisit the moving least squares (MLS) approximation scheme on the sphere \(\mathbb S^{d-1} \subset {\mathbb R}^d\), where \(d>1\). It is well known that using the spherical harmonics up to degree \(L \in {\mathbb N}\) as ansatz space yields for functions in \(\mathcal {C}^{L+1}(\mathbb S^{d-1})\) the approximation order \(\mathcal {O}\left( h^{L+1} \right) \), where h denotes the fill distance
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A unified local projection-based stabilized virtual element method for the coupled Stokes-Darcy problem Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-21 Sudheer Mishra, E. Natarajan
In this work, we propose and analyze a new stabilized virtual element method for the coupled Stokes-Darcy problem with Beavers-Joseph-Saffman interface condition on polygonal meshes. We derive two variants of local projection stabilization methods for the coupled Stokes-Darcy problem. The significance of local projection-based stabilization terms is that they provide reasonable control of the pressure
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Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization Found. Comput. Math. (IF 2.5) Pub Date : 2024-10-18 Sören Bartels, Alex Kaltenbach
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A pressure-residual augmented GLS stabilized method for a type of Stokes equations with nonstandard boundary conditions Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-14 Huoyuan Duan, Roger C. E. Tan, Duowei Zhu
With local pressure-residual stabilizations as an augmentation to the classical Galerkin/least-squares (GLS) stabilized method, a new locally evaluated residual-based stabilized finite element method is proposed for a type of Stokes equations from the incompressible flows. We focus on the study of a type of nonstandard boundary conditions involving the mixed tangential velocity and pressure Dirichlet
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A stochastic perturbation analysis of the QR decomposition and its applications Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-02 Tianru Wang, Yimin Wei
The perturbation of the QR decompostion is analyzed from the probalistic point of view. The perturbation error is approximated by a first-order perturbation expansion with high probability where the perturbation is assumed to be random. Different from the previous normwise perturbation bounds using the Frobenius norm, our techniques are used to develop the spectral norm, as well as the entry-wise perturbation
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An electrical engineering perspective on naturality in computational physics Adv. Comput. Math. (IF 1.7) Pub Date : 2024-10-01 P. Robert Kotiuga, Valtteri Lahtinen
We look at computational physics from an electrical engineering perspective and suggest that several concepts of mathematics, not so well-established in computational physics literature, present themselves as opportunities in the field. We discuss elliptic complexes and highlight the category theoretical background and its role as a unifying language between algebraic topology, differential geometry
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The Gromov–Wasserstein Distance Between Spheres Found. Comput. Math. (IF 2.5) Pub Date : 2024-09-16 Shreya Arya, Arnab Auddy, Ranthony A. Clark, Sunhyuk Lim, Facundo Mémoli, Daniel Packer
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Unbiasing Hamiltonian Monte Carlo Algorithms for a General Hamiltonian Function Found. Comput. Math. (IF 2.5) Pub Date : 2024-09-16 T. Lelièvre, R. Santet, G. Stoltz
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Maximal volume matrix cross approximation for image compression and least squares solution Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-16 Kenneth Allen, Ming-Jun Lai, Zhaiming Shen
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume submatrices. More precisely, we present a new proof of the classic estimate of the inequality with an improved constant. Also, we present a family of greedy maximal
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Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-14 Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab
The distribution of centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds is determined by their covariance operators. We consider centered GRFs given as variational solutions to coloring operator equations driven by spatial white noise, with an elliptic self-adjoint pseudodifferential coloring operator from
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Improved a posteriori error bounds for reduced port-Hamiltonian systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-11 Johannes Rettberg, Dominik Wittwar, Patrick Buchfink, Robin Herkert, Jörg Fehr, Bernard Haasdonk
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical
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Interpolating refinable functions and $$n_s$$ -step interpolatory subdivision schemes Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-05 Bin Han
Standard interpolatory subdivision schemes and their underlying interpolating refinable functions are of interest in CAGD, numerical PDEs, and approximation theory. Generalizing these notions, we introduce and study \(n_s\)-step interpolatory \(\textsf{M}\)-subdivision schemes and their interpolating \(\textsf{M}\)-refinable functions with \(n_s\in \mathbb {N}\cup \{\infty \}\) and a dilation factor
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SVD-based algorithms for tensor wheel decomposition Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-05 Mengyu Wang, Honghua Cui, Hanyu Li
Tensor wheel (TW) decomposition combines the popular tensor ring and fully connected tensor network decompositions and has achieved excellent performance in tensor completion problem. A standard method to compute this decomposition is the alternating least squares (ALS). However, it usually suffers from slow convergence and numerical instability. In this work, the fast and robust SVD-based algorithms
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Signed Barcodes for Multi-parameter Persistence via Rank Decompositions and Rank-Exact Resolutions Found. Comput. Math. (IF 2.5) Pub Date : 2024-09-04 Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot
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Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-09-02 Desong Kong, Jie Shen, Li-Lian Wang, Shuhuang Xiang
In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulting from the Legendre dual-Petrov-Galerkin (LDPG) method for the mth-order initial value problem (IVP): \(u^{(m)}(t)=\sigma u(t),\, t\in (-1,1)\) with constant \(\sigma \not =0\) and usual initial conditions at t\(=-1,\) are associated with the generalised Bessel polynomials (GBPs). In particular
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On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-28 Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino
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Families of annihilating skew-selfadjoint operators and their connection to Hilbert complexes Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-27 Dirk Pauly, Rainer Picard
In this short note we show that Hilbert complexes are strongly related to what we shall call annihilating sets of skew-selfadjoint operators. This provides for a new perspective on the classical topic of Hilbert complexes viewed as families of commuting normal operators.
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New Ramsey Multiplicity Bounds and Search Heuristics Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-26 Olaf Parczyk, Sebastian Pokutta, Christoph Spiegel, Tibor Szabó
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Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-23 Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
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Learning Time-Scales in Two-Layers Neural Networks Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-22 Raphaël Berthier, Andrea Montanari, Kangjie Zhou
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Computing eigenvalues of quasi-rational Said–Ball–Vandermonde matrices Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-22 Xiaoxiao Ma, Yingqing Xiao
This paper focuses on computing the eigenvalues of the generalized collocation matrix of the rational Said–Ball basis, also called as the quasi-rational Said–Ball–Vandermonde (q-RSBV) matrix, with high relative accuracy. To achieve this, we propose explicit expressions for the minors of the q-RSBV matrix and develop a high-precision algorithm to compute these parameters. Additionally, we present perturbation
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Morley type virtual element method for von Kármán equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-22 Devika Shylaja, Sarvesh Kumar
This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error
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Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-19 Bernard Kapidani, Melina Merkel, Sebastian Schöps, Rafael Vázquez
Common formulations of the eddy current problem involve either vector or scalar potentials, each with its own advantages and disadvantages. An impasse arises when using scalar potential-based formulations in the presence of conductors with non-trivial topology. A remedy is to augment the approximation spaces with generators of the first cohomology group. Most existing algorithms for this require a
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The Universal Equivariance Properties of Exotic Aromatic B-Series Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-16 Adrien Laurent, Hans Munthe-Kaas
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Approximations of Dispersive PDEs in the Presence of Low-Regularity Randomness Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-15 Yvonne Alama Bronsard, Yvain Bruned, Katharina Schratz
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Convergence analysis of the Dirichlet-Neumann Waveform Relaxation algorithm for time fractional sub-diffusion and diffusion-wave equations in heterogeneous media Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-14 Soura Sana, Bankim C Mandal
This article presents a comprehensive study on the convergence behavior of the Dirichlet-Neumann Waveform Relaxation algorithm applied to solve the time fractional sub-diffusion and diffusion-wave equations in multiple subdomains, considering the presence of some heterogeneous media. Our analysis focuses on estimating the convergence rate of the algorithm and investigates how this estimate varies with
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Global Convergence of Hessenberg Shifted QR I: Exact Arithmetic Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-13 Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava
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Frame-normalizable sequences Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-09 Pu-Ting Yu
Let H be a separable Hilbert space and let \(\{x_{n}\}\) be a sequence in H that does not contain any zero elements. We say that \(\{x_{n}\}\) is a Bessel-normalizable or frame-normalizable sequence if the normalized sequence \({\bigl \{\frac{x_n}{\Vert x_n\Vert }\bigr \}}\) is a Bessel sequence or a frame for H, respectively. In this paper, several necessary and sufficient conditions for sequences
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SlabLU: a two-level sparse direct solver for elliptic PDEs Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-09 Anna Yesypenko, Per-Gunnar Martinsson
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Education SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Hélène Frankowska
SIAM Review, Volume 66, Issue 3, Page 573-573, May 2024. In this issue the Education section presents “Combinatorial and Hodge Laplacians: Similarities and Differences,” by Emily Ribando-Gros, Rui Wang, Jiahui Chen, Yiying Tong, and Guo-Wei Wei. Combinatorial Laplacians and their spectra are important tools in the study of molecular stability, electrical networks, neuroscience, deep learning, signal
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Operator Learning Using Random Features: A Tool for Scientific Computing SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Nicholas H. Nelsen, Andrew M. Stuart
SIAM Review, Volume 66, Issue 3, Page 535-571, May 2024. Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing, which may often be framed in terms of operators mapping between spaces of functions. Building on the classical
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Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Abigail Hickok, Benjamin Jarman, Michael Johnson, Jiajie Luo, Mason A. Porter
SIAM Review, Volume 66, Issue 3, Page 481-500, May 2024. It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability of transportation, and ease of travel. We use persistent homology, which is a tool from topological
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Research Spotlights SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Stefan M. Wild
SIAM Review, Volume 66, Issue 3, Page 479-479, May 2024. Equitable distribution of geographically dispersed resources presents a significant challenge, particularly in defining quantifiable measures of equity. How can we optimally allocate polling sites or hospitals to serve their constituencies? This issue's first Research Spotlight, “Persistent Homology for Resource Coverage: A Case Study of Access
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Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-08 Liyao Hao, Wenyi Tian
In this paper, we propose and analyze a second-order time-stepping numerical scheme for the inhomogeneous backward fractional Feynman-Kac equation with nonsmooth initial data. The complex parameters and time-space coupled Riemann-Liouville fractional substantial integral and derivative in the equation bring challenges on numerical analysis and computations. The nonlocal operators are approximated by
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Balanced truncation for quadratic-bilinear control systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-08 Peter Benner, Pawan Goyal
We discuss model order reduction (MOR) for large-scale quadratic-bilinear (QB) systems based on balanced truncation. The method for linear systems mainly involves the computation of the Gramians of the system, namely reachability and observability Gramians. These Gramians are extended to a general nonlinear setting in Scherpen (Systems Control Lett. 21, 143-153 1993). These formulations of Gramians
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Combinatorial and Hodge Laplacians: Similarities and Differences SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Emily Ribando-Gros, Rui Wang, Jiahui Chen, Yiying Tong, Guo-Wei Wei
SIAM Review, Volume 66, Issue 3, Page 575-601, May 2024. As key subjects in spectral geometry and combinatorial graph theory, respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing the topological dimension and geometric shape of data and in their realization of diffusion and minimization of harmonic measures. It is believed that they also both
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Cardinality Minimization, Constraints, and Regularization: A Survey SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi, Alexandra Schwartz
SIAM Review, Volume 66, Issue 3, Page 403-477, May 2024. We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and we give concrete examples from diverse application fields such as signal and image processing, portfolio selection, and machine learning. The paper
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When Data Driven Reduced Order Modeling Meets Full Waveform Inversion SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Liliana Borcea, Josselin Garnier, Alexander V. Mamonov, Jörn Zimmerling
SIAM Review, Volume 66, Issue 3, Page 501-532, May 2024. Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively studied inverse problem with a wide range of applications, but the existing inversion methodologies are
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Book Reviews SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Anita T. Layton
SIAM Review, Volume 66, Issue 3, Page 605-615, May 2024. The theme of this collection of book reviews is arguably about the “usefulness” of mathematics, or how we can try to understand aspects of our world by developing mathematical or data-driven models. Thus, it is fitting that our featured review is written by John Stillwell, on the book Why Does Math Work . . . If It's Not Real?, written by Dragan
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Survey and Review SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 Marlis Hochbruck
SIAM Review, Volume 66, Issue 3, Page 401-401, May 2024. In “Cardinality Minimization, Constraints, and Regularization: A Survey," Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi, and Alexandra Schwartz consider a class of optimization problems that involve the cardinality of variable vectors in constraints or in the objective function. Such problems have many important applications, e.g., medical
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SIGEST SIAM Rev. (IF 10.8) Pub Date : 2024-08-08 The Editors
SIAM Review, Volume 66, Issue 3, Page 533-533, May 2024. The SIGEST article in this issue is “Operator Learning Using Random Features: A Tool for Scientific Computing,” by Nicholas H. Nelsen and Andrew M. Stuart. This work considers the problem of operator learning in infinite-dimensional Banach spaces through the use of random features. The driving application is the approximation of solution operators
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Convergence of Numerical Methods for the Navier–Stokes–Fourier System Driven by Uncertain Initial/Boundary Data Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-06 Eduard Feireisl, Mária Lukáčová-Medvid’ová, Bangwei She, Yuhuan Yuan
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Weights for moments’ geometrical localization: a canonical isomorphism Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-06 Ana Alonso Rodríguez, Jessika Camaño, Eduardo De Los Santos, Francesca Rapetti
This paper deals with high order Whitney forms. We define a canonical isomorphism between two sets of degrees of freedom. This allows to geometrically localize the classical degrees of freedom, the moments, over the elements of a simplicial mesh. With such a localization, it is thus possible to associate, even with moments, a graph structure relating a field with its potential.
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Polynomial and Rational Measure Modifications of Orthogonal Polynomials via Infinite-Dimensional Banded Matrix Factorizations Found. Comput. Math. (IF 2.5) Pub Date : 2024-08-05 Timon S. Gutleb, Sheehan Olver, Richard Mikaël Slevinsky
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Online identification and control of PDEs via reinforcement learning methods Adv. Comput. Math. (IF 1.7) Pub Date : 2024-08-01 Alessandro Alla, Agnese Pacifico, Michele Palladino, Andrea Pesare
We focus on the control of unknown partial differential equations (PDEs). The system dynamics is unknown, but we assume we are able to observe its evolution for a given control input, as typical in a reinforcement learning framework. We propose an algorithm based on the idea to control and identify on the fly the unknown system configuration. In this work, the control is based on the state-dependent
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Two-grid stabilized finite element methods with backtracking for the stationary Navier-Stokes equations Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-30 Jing Han, Guangzhi Du
Based on local Gauss integral technique and backtracking technique, this paper presents and studies three kinds of two-grid stabilized finite element algorithms for the stationary Navier-Stokes equations. The proposed methods consist of deducing a coarse solution on the nonlinear system, updating the solution on a fine mesh via three different methods, and solving a linear correction problem on the
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Averaging property of wedge product and naturality in discrete exterior calculus Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-31 Mark D. Schubel, Daniel Berwick-Evans, Anil N. Hirani
In exterior calculus on smooth manifolds, the exterior derivative and wedge products are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial cochains play the role of discrete forms, the coboundary operator serves as the discrete exterior derivative, and an antisymmetrized cup-like product provides a
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Stable Liftings of Polynomial Traces on Tetrahedra Found. Comput. Math. (IF 2.5) Pub Date : 2024-07-29 Charles Parker, Endre Süli
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Resonances as a Computational Tool Found. Comput. Math. (IF 2.5) Pub Date : 2024-07-26 Frédéric Rousset, Katharina Schratz
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full equation into a series of simpler subproblems (e.g., splitting methods). In many situations these classical schemes allow a precise and efficient approximation. This
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Analysis of Langevin Monte Carlo from Poincaré to Log-Sobolev Found. Comput. Math. (IF 2.5) Pub Date : 2024-07-26 Sinho Chewi, Murat A. Erdogdu, Mufan Li, Ruoqi Shen, Matthew S. Zhang
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Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-23 Gabriel Nóbrega Bufolo, Yuri Dumaresq Sobral
The discrete element method (DEM) is a numerical technique widely used to simulate granular materials. The temporal evolution of these simulations is often performed using a Verlet-type algorithm, because of its second order and its desirable property of better energy conservation. However, when dissipative forces are considered in the model, such as the nonlinear Kuwabara-Kono model, the Verlet method
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The $$L_q$$ -weighted dual programming of the linear Chebyshev approximation and an interior-point method Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-22 Yang Linyi, Zhang Lei-Hong, Zhang Ya-Nan
Given samples of a real or complex-valued function on a set of distinct nodes, the traditional linear Chebyshev approximation is to compute the minimax approximation on a prescribed linear functional space. Lawson’s iteration is a classical and well-known method for the task. However, Lawson’s iteration converges only linearly and in many cases, the convergence is very slow. In this paper, relying
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Randomized greedy magic point selection schemes for nonlinear model reduction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-22 Ralf Zimmermann, Kai Cheng
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A Polynomial Time Iterative Algorithm for Matching Gaussian Matrices with Non-vanishing Correlation Found. Comput. Math. (IF 2.5) Pub Date : 2024-07-22 Jian Ding, Zhangsong Li
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Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-19 Quirin Aumann, Steffen W. R. Werner
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal interpolation points and the appropriate size of the reduced-order model. An approach that addresses the first problem for linear, unstructured systems is the iterative
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Quantitative Stability of the Pushforward Operation by an Optimal Transport Map Found. Comput. Math. (IF 2.5) Pub Date : 2024-07-19 Guillaume Carlier, Alex Delalande, Quentin Mérigot
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On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-19 Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang
Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been given in Greif et al. [SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1071–1087]. In this work, we extend the results of Greif et al. to singular skew-symmetric linear
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A continuation method for fitting a bandlimited curve to points in the plane Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-16 Mohan Zhao, Kirill Serkh
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in \(\mathbb {R}^{2}\). The main idea is to smooth the parametrization of the curve by iteratively filtering the Fourier or Chebyshev coefficients of both the derivative of the arc-length function and the tangential angle of the curve and applying smooth
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Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-16 Hong Zhu, Xiaoxia Liu, Lin Huang, Zhaosong Lu, Jian Lu, Michael K. Ng
Multi-dimensional images can be viewed as tensors and have often embedded a low-rankness property that can be evaluated by tensor low-rank measures. In this paper, we first introduce a tensor low-rank and sparsity measure and then propose low-rank and sparsity models for tensor completion, tensor robust principal component analysis, and tensor denoising. The resulting tensor recovery models are further
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Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation Adv. Comput. Math. (IF 1.7) Pub Date : 2024-07-16 Julian Koellermeier, Philipp Krah, Jonas Kusch
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaranteeing physical properties like mass conservation. In this paper, we develop the first model reduction