Search Results - "Numerical methods for low-rank matrix approximation"

Structure-Aware Analyses and Algorithms for Interpolative Decompositions: Structure-aware analyses and algorithms for interpolative decompositions

Authors: Robin Armstrong Alex Buzali Anil Damle

Source: SIAM Journal on Scientific Computing. 47:A1527-A1554

Subject Terms: low-rank approximation, randomized SVD, 65F55, 68W20, stable rank, Randomized algorithms, interpolative decomposition, FOS: Mathematics, Numerical methods for low-rank matrix approximation, matrix compression, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), rank-revealing QR factorization, coherence

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Access URL: http://arxiv.org/abs/2310.09452
https://zbmath.org/8037167
https://doi.org/10.1137/23m1610811

Mixed Precision HODLR Matrices: Mixed precision HODLR matrices

Authors: Erin Carson Xinye Chen Xiaobo Liu et al.

Contributors: Erin Carson Xinye Chen Xiaobo Liu et al.

Source: SIAM Journal on Scientific Computing. 47:A1408-A1435

Subject Terms: hierarchical matrices, Hierarchical matrices, 65D18, Roundoff error, mixed precision computing, Analysis of algorithms and problem complexity, 65G50, 65F55, 68Q25, 65D18, 68Q25, Numerical methods for low-rank matrix approximation, matrix compression, matrix computations AMS subject classifications. 65G50, Numerical Analysis (math.NA), [INFO] Computer Science [cs], Hierarchical matrices mixed precision computing matrix computations AMS subject classifications. 65G50 65F55 68Q25 65D18, Numerical aspects of computer graphics, image analysis, and computational geometry, FOS: Mathematics, Mathematics - Numerical Analysis, matrix computations, 65F55

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Access URL: http://arxiv.org/abs/2407.21637
https://hal.science/hal-05066310v1
https://doi.org/10.1137/24m1683925
https://hal.science/hal-05066310v1/document

Truncated QR Factorization with Pivoting in Mixed Precision: Truncated QR factorization with pivoting in mixed precision

Authors: Buttari, Alfredo Mary, Theo Pacteau, André

Contributors: Buttari, Alfredo Mary, Theo Pacteau, André

Source: SIAM Journal on Scientific Computing. 47:B382-B401

Subject Terms: mixed precision, [INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS], Roundoff error, [INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA], Mixed-precision algorithms, low-rank approximations, QR factorization, Numerical methods for low-rank matrix approximation, matrix compression, [INFO.INFO-AO] Computer Science [cs]/Computer Arithmetic

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Pseudospectrum of Kronecker product and stability analysis of tensor equations

Authors: G. Krishna Kumar R. J. Renjini

Source: The Journal of Analysis. 33:949-970

Subject Terms: S-pseudospectrum, Eigenvalues, singular values, and eigenvectors, Numerical solutions to overdetermined systems, pseudoinverses, even-order tensor, Kronecker product, Einstein product, Multilinear algebra, tensor calculus, tensor equation, Numerical methods for low-rank matrix approximation, matrix compression, stability, Vector and tensor algebra, theory of invariants

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An a priori method for estimating the informativeness of the configuration of sensor placement when solving inverse problems of remote sensing

Authors: Dmitry V. Lukyanenko Bulat I. Valiakhmetov Eugene E. Tyrtyshnikov et al.

Source: Journal of Inverse and Ill-posed Problems. 33:15-30

Subject Terms: low-rank approximation, optimal sensor placement, matrix-cross method, optimal number of measurements, informativeness criterion, Numerical methods for low-rank matrix approximation, matrix compression, linear inverse problem, mosaic-skeleton approximation, compression rate of matrix, Numerical methods for inverse problems for integral equations

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Collocation methods for nonlinear differential equations on low-rank manifolds

Authors: Alec Dektor

Source: Linear Algebra and its Applications. 705:143-184

Subject Terms: low-rank approximation, tensor cross approximation, Numerical linear algebra, Numerical & Computational Mathematics, Mathematical sciences, Numerical methods for low-rank matrix approximation, matrix compression, tensor differential equations, FOS: Physical sciences, Numerical Analysis (math.NA), Low-rank approximation, Tensor train format, time-dependent tensors, Computational Physics (physics.comp-ph), Tensor differential equations, Mathematical Sciences, Time-dependent tensors, Engineering, Information and Computing Sciences, Tensor cross approximation, Multilinear algebra, tensor calculus, FOS: Mathematics, Mathematics - Numerical Analysis, Physics - Computational Physics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, tensor train format

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Access URL: http://arxiv.org/abs/2402.18721
https://escholarship.org/uc/item/1sz9921z
https://escholarship.org/content/qt1sz9921z/qt1sz9921z.pdf

Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations: Efficient bounds and estimates for canonical angles in randomized subspace approximations

Authors: Yijun Dong Per-Gunnar Martinsson Yuji Nakatsukasa

Source: SIAM Journal on Matrix Analysis and Applications. 45:1978-2006

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, singular vectors, Eigenvalues, singular values, and eigenvectors, canonical angles, 15A18, 15A42, 65F15, 68W20, randomized subspace iteration, FOS: Mathematics, Numerical methods for low-rank matrix approximation, matrix compression, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, Inequalities involving eigenvalues and eigenvectors, 01 natural sciences

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Access URL: http://arxiv.org/abs/2211.04676
https://zbmath.org/7947701
https://doi.org/10.1137/23m1584733

Low-rank exponential integrators for stiff differential Riccati equations

Authors: Hao Chen Alfio Borzì

Source: Advances in Computational Mathematics. 51

Subject Terms: differential Riccati equation, exponential integrator, Linear-quadratic optimal control problems, Numerical methods for low-rank matrix approximation, matrix compression, error estimate, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for ordinary differential equations, low-rank

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Access URL: https://zbmath.org/8028903
https://doi.org/10.1007/s10444-025-10228-w

A symmetric ADMM-type algorithm for robust tensor completion problems using a regularized SCAD-Schatten-p model with application in color image and video recovery

Authors: Zhang, Zhechen Liu, Sanyang Liu, Lixia et al.

Source: Journal of Computational and Applied Mathematics. 466:116604

Subject Terms: Numerical optimization and variational techniques, symmetric ADMM, Schatten-p norm, SCAD function, Numerical aspects of computer graphics, image analysis, and computational geometry, Multilinear algebra, tensor calculus, Numerical methods for low-rank matrix approximation, matrix compression, Nonconvex programming, global optimization, robust tensor completion, total variation regularization

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Access URL: https://zbmath.org/8031355
https://doi.org/10.1016/j.cam.2025.116604

Learning tensor networks with tensor cross interpolation: New algorithms and libraries: Learning tensor networks with tensor cross interpolation: new algorithms and libraries

Authors: Yuriel Núñez Fernández Marc K Ritter Matthieu Jeannin et al.

Contributors: Yuriel Núñez Fernández Marc K Ritter Matthieu Jeannin et al.

Source: SciPost Physics, Vol 18, Iss 3, p 104 (2025)

Subject Terms: Condensed Matter - Strongly Correlated Electrons, Strongly Correlated Electrons (cond-mat.str-el), [SPI] Engineering Sciences [physics], Physics, QC1-999, 4. Education, Multilinear algebra, tensor calculus, Numerical methods for low-rank matrix approximation, matrix compression, FOS: Physical sciences, Computational Physics (physics.comp-ph), Physics - Computational Physics, [PHYS] Physics [physics]

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Access URL: http://arxiv.org/abs/2407.02454
https://zbmath.org/8034112
https://doi.org/10.21468/scipostphys.18.3.104
https://doaj.org/article/aad33ab366cf47b8a49668e71853a813
https://hal.science/hal-04877055v1
https://doi.org/10.21468/scipostphys.18.3.104

Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method

Authors: Shubhaditya Burela Philipp Krah Julius Reiss

Source: Advances in Computational Mathematics. 51

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, shifted proper orthogonal decomposition, 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik, Fluid Dynamics (physics.flu-dyn), Numerical methods for low-rank matrix approximation, matrix compression, deep learning, FOS: Physical sciences, Physics - Fluid Dynamics, Numerical Analysis (math.NA), wildland fires, model order reduction, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, artificial neural networks, data-driven models, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2304.14872
https://zbmath.org/8015907
https://doi.org/10.1007/s10444-025-10220-4

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations: Robust implicit adaptive low rank time-stepping methods for matrix differential equations

Authors: Appelö, Daniel Cheng, Yingda

Source: Journal of Scientific Computing. 102

Subject Terms: convergence, matrix differential equation, Numerical methods for matrix equations, dynamic low rank approximation, Matrix equations and identities, FOS: Mathematics, Numerical methods for low-rank matrix approximation, matrix compression, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), stability

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Access URL: http://arxiv.org/abs/2402.05347
https://zbmath.org/7983283
https://doi.org/10.1007/s10915-025-02808-1

Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides: Communication avoiding block low-rank parallel multifrontal triangular solve with many right-hand sides

Authors: Amestoy, Patrick Boiteau, Olivier Buttari, Alfredo et al.

Contributors: Amestoy, Patrick Boiteau, Olivier Buttari, Alfredo et al.

Source: SIAM Journal on Matrix Analysis and Applications. 45:148-166

Subject Terms: block low-rank matrices, linear systems, Numerical methods for low-rank matrix approximation, matrix compression, [MATH] Mathematics [math], Parallel numerical computation, [INFO] Computer Science [cs], Direct numerical methods for linear systems and matrix inversion, communication avoiding algorithms, Computational methods for sparse matrices, LU factorization, low-rank approximations, numerical linear algebra, data sparse matrices, [INFO]Computer Science [cs], triangular solve, [MATH]Mathematics [math]

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Access URL: https://zbmath.org/7791523
https://doi.org/10.1137/23m1568600
https://hal.science/hal-04082415v1/document
https://doi.org/10.1137/23m1568600
https://hal.science/hal-04082415v1

Euclidean Representation of Low-Rank Matrices and Its Geometric Properties: Euclidean representation of low-rank matrices and its geometric properties

Authors: Fangzheng Xie

Source: SIAM Journal on Matrix Analysis and Applications. 44:822-866

Subject Terms: intrinsic perturbation analysis, Euclidean representation, Cayley parameterization, Numerical methods for low-rank matrix approximation, matrix compression, low-rank matrix geometry, Basic linear algebra, low-rank matrix manifold, Multivariate distribution of statistics

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Access URL: https://zbmath.org/7707726
https://doi.org/10.1137/22m1489125

WBEM-based analysis of band structures of solid-solid and fluid-fluid phononic crystals with frequency-independent fundamental solutions

Authors: Wei, Qi Xiang, Jiawei Zhu, Weiping et al.

Source: Engineering Analysis with Boundary Elements. 151:439-456

Subject Terms: Boundary element methods for initial value and initial-boundary value problems involving PDEs, domain integral, matrix compression, band structure, Numerical methods for wavelets, wavelet-based boundary element method, Numerical methods for low-rank matrix approximation, B-spline wavelet on the interval, phononic crystals, Boundary element methods applied to problems in solid mechanics

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Towards dynamical low-rank approximation for neutrino kinetic equations. Part I: Analysis of an idealized relaxation model: Towards dynamical low-rank approximation for neutrino kinetic equations. I: Analysis of an idealized relaxation model

Authors: Yin, Peimeng Endeve, Eirik Hauck, Cory D. et al.

Source: Mathematics of Computation.

Subject Terms: radiation transport, semi-implicit time integration, unconventional integrator, 0103 physical sciences, Numerical methods for low-rank matrix approximation, matrix compression, kinetic equations, discontinuous Galerkin method, Stability and convergence of numerical methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 0101 mathematics, dynamical low-rank approximation, 01 natural sciences

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Access URL: https://zbmath.org/7984329
https://doi.org/10.1090/mcom/3997

SlabLU: a two-level sparse direct solver for elliptic PDEs

Authors: Anna Yesypenko Per-Gunnar Martinsson

Source: Advances in Computational Mathematics. 50

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Numerical Analysis, Random matrices (algebraic aspects), GPU, Numerical methods for low-rank matrix approximation, matrix compression, high-order discretization, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, multifrontal solver, 01 natural sciences, Factorization of matrices, direct solver, Computational methods for sparse matrices, Numerical algorithms for specific classes of architectures, Boundary value problems for second-order elliptic equations, sparse direct solver, FOS: Mathematics, Spectral, collocation and related methods for boundary value problems involving PDEs, randomized linear algebra, Helmholtz equation, 0101 mathematics

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Access URL: http://arxiv.org/abs/2211.07572

Overlapping Domain Decomposition Preconditioner for Integral Equations: Overlapping domain decomposition preconditioner for integral equations

Authors: Chao Chen George Biros

Source: SIAM Journal on Scientific Computing. 44:A3617-A3644

Subject Terms: hierarchical matrices, integral equations, Multigrid methods, domain decomposition for boundary value problems involving PDEs, Numerical computation of matrix norms, conditioning, scaling, fast direct solvers, Numerical methods for low-rank matrix approximation, matrix compression, Fredholm integral equations, Numerical Analysis (math.NA), Numerical methods for integral equations, 01 natural sciences, Integro-partial differential equations, symmetric positive-definite preconditioners, overlapping domain decomposition, FOS: Mathematics, Preconditioners for iterative methods, Mathematics - Numerical Analysis, 0101 mathematics

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Access URL: http://arxiv.org/abs/2108.12574
https://zbmath.org/7617465
https://doi.org/10.1137/21m1442917

Approximating a branch of solutions to the Navier–Stokes equations by reduced-order modeling: Approximating a branch of solutions to the Navier-Stokes equations by reduced-order modeling

Authors: Maxim A. Olshanskii Leo G. Rebholz

Source: Journal of Computational Physics. 524:113728

Subject Terms: Navier-Stokes equations for incompressible viscous fluids, Fluid Dynamics (physics.flu-dyn), Numerical methods for low-rank matrix approximation, matrix compression, FOS: Physical sciences, Physics - Fluid Dynamics, Computational Physics (physics.comp-ph), 76D17, 76D05, 65M60, Physics - Computational Physics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: http://arxiv.org/abs/2405.03796

Scalable resolvent analysis for three-dimensional flows

Authors: Ali Farghadan Eduardo Martini Aaron Towne

Source: Journal of Computational Physics. 524:113695

Subject Terms: Turbulence, algorithm, randomized singular value decomposition, resolvent analysis, Fluid Dynamics (physics.flu-dyn), Numerical methods for low-rank matrix approximation, matrix compression, FOS: Physical sciences, Physics - Fluid Dynamics, PDEs in connection with fluid mechanics, time stepping, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: http://arxiv.org/abs/2309.04617
https://zbmath.org/7996110
https://doi.org/10.1016/j.jcp.2024.113695