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Highly localized RBF Lagrange functions for finite difference methods on spheres BIT Numer. Math. (IF 1.5) Pub Date : 2024-03-15 W. Erb, T. Hangelbroek, F. J. Narcowich, C. Rieger, J. D. Ward
The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the sphere can be used to create a numerically feasible, stable finite difference method based on radial basis functions (an RBF-FD-like method). For certain classes of PDEs this approach leads to rigorous convergence estimates for stencils which grow moderately with increasing discretization fineness.
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Bounded perturbations resilient iterative methods for linear systems and least squares problems: operator-based approaches, analysis, and performance evaluation BIT Numer. Math. (IF 1.5) Pub Date : 2024-03-05 Mokhtar Abbasi, Touraj Nikazad
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The variable two-step BDF method for parabolic equations BIT Numer. Math. (IF 1.5) Pub Date : 2024-03-01 Georgios Akrivis, Minghua Chen, Jianxing Han, Fan Yu, Zhimin Zhang
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A unified immersed finite element error analysis for one-dimensional interface problems BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-29 Slimane Adjerid, Tao Lin, Haroun Meghaichi
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Admissible subspaces and the subspace iteration method BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-28
Abstract In this work we revisit the convergence analysis of the Subspace Iteration Method (SIM) for the computation of approximations of a matrix A by matrices of rank h. Typically, the analysis of convergence of these low-rank approximations has been obtained by first estimating the (angular) distance between the subspaces produced by the SIM and the dominant subspaces of A. It has been noticed that
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Singularity swap quadrature for nearly singular line integrals on closed curves in two dimensions BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-27 Ludvig af Klinteberg
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Structured eigenvalue backward errors for rational matrix functions with symmetry structures BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-17 Anshul Prajapati, Punit Sharma
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Convergence and superconvergence of a fractional collocation method for weakly singular Volterra integro-differential equations BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-12
Abstract A collocation method for the numerical solution of Volterra integro-differential equations with weakly singular kernels, based on piecewise polynomials of fractional order, is constructed and analysed. Typical exact solutions of this class of problems have a weak singularity at the initial time \(t=0\) . A rigorous error analysis of our method shows that, with an appropriate choice of the
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A convolution quadrature using derivatives and its application BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-09 Hao Ren, Junjie Ma, Huilan Liu
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A posteriori error estimates for a dual finite element method for singularly perturbed reaction–diffusion problems BIT Numer. Math. (IF 1.5) Pub Date : 2024-02-05 JaEun Ku, Martin Stynes
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Improved uniform error bounds on parareal exponential algorithm for highly oscillatory systems BIT Numer. Math. (IF 1.5) Pub Date : 2024-01-31 Bin Wang, Yaolin Jiang
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On the stability radius for linear time-delay systems BIT Numer. Math. (IF 1.5) Pub Date : 2024-01-30
Abstract The exponential function that appears in the formula of the stability radius of linear time-delay differential systems is approximated by its Padé approximant. This reduces the computation of the level sets of singular values in the stability radius formula to the computation of imaginary eigenvalues of special matrix polynomials. Then a bisection method is used for computing lower and upper
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Incremental algorithms for truncated higher-order singular value decompositions BIT Numer. Math. (IF 1.5) Pub Date : 2024-01-08 Chao Zeng, Michael K. Ng, Tai-Xiang Jiang
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A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities BIT Numer. Math. (IF 1.5) Pub Date : 2024-01-04 Sergio Amat, David Levin, Juan Ruiz-Álvarez, Dionisio F. Yáñez
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Well-posedness and finite element approximation of mixed dimensional partial differential equations BIT Numer. Math. (IF 1.5) Pub Date : 2023-12-29 Fredrik Hellman, Axel Målqvist, Malin Mosquera
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Randomized Kaczmarz algorithm with averaging and block projection BIT Numer. Math. (IF 1.5) Pub Date : 2023-12-12 Zeyi Zhang, Dong Shen
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Positivity-preserving truncated Euler–Maruyama method for generalised Ait-Sahalia-type interest model BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-27 Shounian Deng, Chen Fei, Weiyin Fei, Xuerong Mao
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Symmetric-conjugate splitting methods for linear unitary problems BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-10 J. Bernier, S. Blanes, F. Casas, A. Escorihuela-Tomàs
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A flexible short recurrence Krylov subspace method for matrices arising in the time integration of port-Hamiltonian systems and ODEs/DAEs with a dissipative Hamiltonian BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-10 Malak Diab, Andreas Frommer, Karsten Kahl
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An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-10 Jiayu Han, Zhimin Zhang
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New structure-preserving mixed finite element method for the stationary MHD equations with magnetic-current formulation BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-01 Xiaodi Zhang, Shitian Dong
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A note on approximate Jacobians of implicit Runge–Kutta methods and convergence of modified Newton iterations BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-01 Laurent O. Jay, Olga Sokratova
We consider the application of implicit Runge–Kutta (IRK) methods to systems of implicit ordinary differential equations (ODEs). We are especially interested in the situation when stiffness arises. We show that the eigenvalues of major families of A-stable implicit Runge–Kutta methods are simple and have non-negative real part. We give necessary and sufficient conditions for the invertibility of approximate
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Gaussian rule for integrals involving Bessel functions BIT Numer. Math. (IF 1.5) Pub Date : 2023-11-01 Eleonora Denich, Paolo Novati
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Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov–Maxwell equations BIT Numer. Math. (IF 1.5) Pub Date : 2023-10-13 Andrés Galindo-Olarte, Juntao Huang, Jennifer Ryan, Yingda Cheng
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Galerkin–Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds BIT Numer. Math. (IF 1.5) Pub Date : 2023-10-11 Annika Lang, Mike Pereira
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Deep neural networks on diffeomorphism groups for optimal shape reparametrization BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-27 Elena Celledoni, Helge Glöckner, Jørgen N. Riseth, Alexander Schmeding
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On the Forsythe conjecture BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-27 Vance Faber, Jörg Liesen, Petr Tichý
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Paige’s Algorithm for solving a class of tensor least squares problem BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-20 Xue-Feng Duan, Yong-Shen Zhang, Qing-Wen Wang, Chun-Mei Li
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A stabilized finite element method on nonaffine grids for time-harmonic Maxwell’s equations BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-19 Zhijie Du, Huoyuan Duan
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Resolving entropy growth from iterative methods BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-15 Viktor Linders, Hendrik Ranocha, Philipp Birken
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Stabilized low-order mixed finite element methods for a Navier-Stokes hemivariational inequality BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-16 Weimin Han, Feifei Jing, Yuan Yao
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Parallel line identification for line-implicit-solvers BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-09 Arne Rempke
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Strong convergence rates of an explicit scheme for stochastic Cahn–Hilliard equation with additive noise BIT Numer. Math. (IF 1.5) Pub Date : 2023-09-04 Meng Cai, Ruisheng Qi, Xiaojie Wang
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Analysis and preconditioning of parameter-robust finite element methods for Biot’s consolidation model BIT Numer. Math. (IF 1.5) Pub Date : 2023-07-25 Jeonghun J. Lee
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Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals BIT Numer. Math. (IF 1.5) Pub Date : 2023-07-24 William Mitchell, Abbie Natkin, Paige Robertson, Marika Sullivan, Xuechen Yu, Chenxin Zhu
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Backward Euler method for stochastic differential equations with non-Lipschitz coefficients driven by fractional Brownian motion BIT Numer. Math. (IF 1.5) Pub Date : 2023-07-07 Hao Zhou, Yaozhong Hu, Yanghui Liu
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Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations BIT Numer. Math. (IF 1.5) Pub Date : 2023-07-03 Hong-lin Liao, Tao Tang, Tao Zhou
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Multilevel Monte Carlo using approximate distributions of the CIR process BIT Numer. Math. (IF 1.5) Pub Date : 2023-06-05 Chao Zheng
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Analysis and simulation of a variational stabilization for the Helmholtz equation with noisy Cauchy data BIT Numer. Math. (IF 1.5) Pub Date : 2023-06-02 Vo Anh Khoa, Nguyen Dat Thuc, Ajith Gunaratne
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A fast randomized algorithm for computing an approximate null space BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-25 Taejun Park, Yuji Nakatsukasa
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Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-25 Daniel Eckhardt, Barbara Verfürth
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Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-22 Philip L. Lederer
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Strong convergence of an adaptive time-stepping Milstein method for SDEs with monotone coefficients BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-22 Cónall Kelly, Gabriel J. Lord, Fandi Sun
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Monte Carlo integration of $$C^r$$ functions with adaptive variance reduction: an asymptotic analysis BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-22 Leszek Plaskota, Paweł Przybyłowicz, Łukasz Stȩpień
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Fast floating-point filters for robust predicates BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-17 Tinko Bartels, Vissarion Fisikopoulos, Martin Weiser
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Low-rank tensor structure preservation in fractional operators by means of exponential sums BIT Numer. Math. (IF 1.5) Pub Date : 2023-05-11 Angelo Casulli, Leonardo Robol
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Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$\beta $$ BIT Numer. Math. (IF 1.5) Pub Date : 2023-04-29 Siegfried M. Rump
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Discretization of inherent ODEs and the geometric integration of DAEs with symmetries BIT Numer. Math. (IF 1.5) Pub Date : 2023-04-29 Peter Kunkel, Volker Mehrmann
Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme suitable for the numerical integration of ODEs. For DAEs with symmetries it is shown that the inherent ODE can be constructed in such a way that it inherits the symmetry
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Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package BIT Numer. Math. (IF 1.5) Pub Date : 2023-04-17 Gerd Steinebach
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On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation BIT Numer. Math. (IF 1.5) Pub Date : 2023-04-13 Tobias Jahnke, Michael Kirn
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Proximal gradient algorithm for nonconvex low tubal rank tensor recovery BIT Numer. Math. (IF 1.5) Pub Date : 2023-04-04 Yanhui Liu, Xueying Zeng, Weiguo Wang
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Product integration rules by the constrained mock-Chebyshev least squares operator BIT Numer. Math. (IF 1.5) Pub Date : 2023-04-03 Francesco Dell’Accio, Domenico Mezzanotte, Federico Nudo, Donatella Occorsio
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On the stability of unevenly spaced samples for interpolation and quadrature BIT Numer. Math. (IF 1.5) Pub Date : 2023-03-31 Annan Yu, Alex Townsend
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Low cardinality positive interior cubature on NURBS-shaped domains BIT Numer. Math. (IF 1.5) Pub Date : 2023-03-17 Alvise Sommariva, Marco Vianello
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AAA interpolation of equispaced data BIT Numer. Math. (IF 1.5) Pub Date : 2023-03-14 Daan Huybrechs, Lloyd N. Trefethen
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Geometric means of quasi-Toeplitz matrices BIT Numer. Math. (IF 1.5) Pub Date : 2023-03-08 Dario A. Bini, Bruno Iannazzo, Jie Meng
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An Hermite-Obreschkoff method for stiff high-index DAE BIT Numer. Math. (IF 1.5) Pub Date : 2023-02-18 Reza Zolfaghari, Nedialko S. Nedialkov
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Singular quadratic eigenvalue problems: linearization and weak condition numbers BIT Numer. Math. (IF 1.5) Pub Date : 2023-02-15 Daniel Kressner, Ivana Šain Glibić
The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are exceptional and standard eigenvalue solvers, such as the QZ algorithm, tend to yield good accuracy despite the inevitable presence of roundoff error
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On Kosloff Tal-Ezer least-squares quadrature formulas BIT Numer. Math. (IF 1.5) Pub Date : 2023-02-12 G. Cappellazzo, W. Erb, F. Marchetti, D. Poggiali
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On the order reduction of approximations of fractional derivatives: an explanation and a cure BIT Numer. Math. (IF 1.5) Pub Date : 2023-02-12 Byron A. Jacobs, Fredrik Laurén, Jan Nordström