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

Συγγραφείς: Robin Armstrong, Alex Buzali, Anil Damle

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2310.09452
https://zbmath.org/8037167
https://doi.org/10.1137/23m1610811

Mixed Precision HODLR Matrices: Mixed precision HODLR matrices

Συγγραφείς: Erin Carson, Xinye Chen, Xiaobo Liu

Συνεισφορές: Chen, Xinye

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Buttari, Alfredo, Mary, Theo, Pacteau, André

Συνεισφορές: Buttari, Alfredo

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml; application/pdf

Pseudospectrum of Kronecker product and stability analysis of tensor equations

Συγγραφείς: G. Krishna Kumar, R. J. Renjini

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

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

Συγγραφείς: Dmitry V. Lukyanenko, Bulat I. Valiakhmetov, Eugene E. Tyrtyshnikov, Anatoly G. Yagola

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Collocation methods for nonlinear differential equations on low-rank manifolds

Συγγραφείς: Alec Dektor

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Yijun Dong, Per-Gunnar Martinsson, Yuji Nakatsukasa

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2211.04676
https://zbmath.org/7947701
https://doi.org/10.1137/23m1584733

Computational Complexity of Decomposing a Symmetric Matrix as a Sum of Positive Semidefinite and Diagonal Matrices

Συγγραφείς: Tunçel, Levent, Vavasis, Stephen A.^{Aff1, IDs10208023096374_cor1}, Xu, Jingye

Πηγή: Foundations of Computational Mathematics: The Journal of the Society for the Foundations of Computational Mathematics. 25(1):223-269

Low-rank exponential integrators for stiff differential Riccati equations

Συγγραφείς: Hao Chen, Alfio Borzì

Πηγή: Advances in Computational Mathematics. 51

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Zhang, Zhechen, Liu, Sanyang, Liu, Lixia, Lin, Zhiping

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Yuriel Núñez Fernández, Marc K Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, Xavier Waintal

Συνεισφορές: Monroy, Eva

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

Θεματικοί όροι: 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]

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Shubhaditya Burela, Philipp Krah, Julius Reiss

Πηγή: Advances in Computational Mathematics. 51

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Appelö, Daniel, Cheng, Yingda

Πηγή: Journal of Scientific Computing. 102

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Amestoy, Patrick, Boiteau, Olivier, Buttari, Alfredo, Gerest, Matthieu, Jézéquel, Fabienne, L’excellent, Jean-Yves, Mary, Theo

Συνεισφορές: Mary, Theo, Mumps Technologies Lyon, EDF R&D (EDF R&D), EDF (EDF), Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Panthéon-Assas

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

Θεματικοί όροι: 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]

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Fangzheng Xie

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Wei, Qi, Xiang, Jiawei, Zhu, Weiping, Hu, Hongjiu

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

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

Συγγραφείς: Yin, Peimeng, Endeve, Eirik, Hauck, Cory D., Schnake, Stefan R.

Πηγή: Mathematics of Computation.

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7984329
https://doi.org/10.1090/mcom/3997

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

Συγγραφείς: Anna Yesypenko, Per-Gunnar Martinsson

Πηγή: Advances in Computational Mathematics. 50

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2211.07572

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

Συγγραφείς: Chao Chen, George Biros

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Maxim A. Olshanskii, Leo G. Rebholz

Πηγή: Journal of Computational Physics. 524:113728

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2405.03796