Search Results - "computation of eigenvalues"

A tridiagonalization-based arbitrary-stride reduction approach for (p,q)-pentadiagonal linear systems: A tridiagonalization-based arbitrary-stride reduction approach for \((p,q)\)-pentadiagonal linear systems

Authors: Yi-Fan Wang Ji-Teng Jia Xin Fan

Source: Applied Numerical Mathematics. 213:77-87

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, \((p, q)\)-pentadiagonal matrix, Diagonalization, Jordan forms, arbitrary-stride reduction, tridiagonalization, extended condition number, linear system, Direct numerical methods for linear systems and matrix inversion, condition number

File Description: application/xml

Access URL: https://zbmath.org/8034918
https://doi.org/10.1016/j.apnum.2025.02.017

Improving Performance of Contour Integral-Based Nonlinear Eigensolvers with Infinite GMRES: Improving performance of contour integral-based nonlinear eigensolvers with infinite GMRES

Authors: Yuqi Liu Jose E. Roman Meiyue Shao

Source: SIAM Journal on Scientific Computing. 47:B595-B617

Subject Terms: Numerical solution of nonlinear eigenvalue and eigenvector problems, Numerical computation of eigenvalues and eigenvectors of matrices, infinite Arnoldi, contour integration, nonlinear eigenvalue problem, FOS: Mathematics, Krylov methods, companion linearization, Mathematics - Numerical Analysis, Numerical Analysis (math.NA)

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Access URL: http://arxiv.org/abs/2403.19309
https://zbmath.org/8037158
https://doi.org/10.1137/24m1650375

Global Convergence of Hessenberg Shifted QR II: Finite Arithmetic: Global convergence of Hessenberg shifted QR. II: Finite arithmetic

Authors: Jess Banks Jorge Garza-Vargas Nikhil Srivastava

Source: SIAM Journal on Matrix Analysis and Applications. 46:1168-1211

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical algorithms for computer arithmetic, etc, shifted QR, numerical linear algebra, Ritz values, nonnormality, dynamical systems

File Description: application/xml

Global Convergence of Hessenberg Shifted QR III: Approximate Ritz Values via Shifted Inverse Iteration: Global convergence of Hessenberg shifted QR. III: Approximate Ritz values via shifted inverse iteration

Authors: Jess Banks Jorge Garza-Vargas Nikhil Srivastava

Source: SIAM Journal on Matrix Analysis and Applications. 46:1212-1246

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, inverse iteration, shifted QR, numerical linear algebra, FOS: Mathematics, Ritz values, nonnormality, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences

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Access URL: http://arxiv.org/abs/2205.06804

Multilinear Singular Value Decomposition–Based Completion with Fibers Observed in a Single Mode: Multilinear singular value decomposition-based completion with fibers observed in a single mode

Authors: Mikael Sørensen Stijn Hendrikx Lieven De Lathauwer

Source: SIAM Journal on Matrix Analysis and Applications. 46:1061-1090

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, structured matrix, missing data, Eigenvalues, singular values, and eigenvectors, multilinear singular value decomposition, Multilinear algebra, tensor calculus, completion, tensor

File Description: application/xml

Access URL: https://zbmath.org/8036733
https://doi.org/10.1137/23m1622830

Some Results On Generalized Antieigenvalue Pairs and Their Associated Antieigenvectors of Certain Class of Linear Two-Parameter Eigenvalue Problems: Some results on generalized antieigenvalue pairs and their associated antieigenvectors of certain class of linear two-parameter eigenvalue problems

Authors: Bora, N. Chutia, B.

Source: Malaysian Journal of Mathematical Sciences. 19:343-359

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, generalized antieigenvectors, Eigenvalues, singular values, and eigenvectors, \(\mathbb{LTEP}\), linearization, Spectrum, resolvent, matrix polynomial, generalized antieigenvalues

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Access URL: https://zbmath.org/8033609
https://doi.org/10.47836/mjms.19.1.18

Riemannian acceleration with preconditioning for symmetric eigenvalue problems

Authors: Shao, Nian Chen, Wenbin

Source: Numerische Mathematik. 157:307-354

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, 15A18, 65F08, 65F15, 65N25, 90C25, FOS: Mathematics, Preconditioners for iterative methods, Mathematics - Numerical Analysis, Numerical Analysis (math.NA)

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Access URL: http://arxiv.org/abs/2309.05143
https://zbmath.org/7978174
https://doi.org/10.1007/s00211-025-01451-0

EPIC: A Provable Accelerated Eigensolver Based on Preconditioning and Implicit Convexity: EPIC: a provable accelerated eigensolver based on preconditioning and implicit convexity

Authors: Nian Shao Wenbin Chen Zhaojun Bai

Source: SIAM Journal on Matrix Analysis and Applications. 46:45-73

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Convex programming, convexity, preconditioning, FOS: Mathematics, eigenvalue problem, Preconditioners for iterative methods, acceleration, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 15A08, 65F08, 65F15, 90C25, 01 natural sciences

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Access URL: http://arxiv.org/abs/2401.11786
https://zbmath.org/7976352
https://doi.org/10.1137/24m1641440

Gradient-Type Subspace Iteration Methods for the Symmetric Eigenvalue Problem: Gradient-type subspace iteration methods for the symmetric eigenvalue problem

Authors: Foivos Alimisis Yousef Saad Bart Vandereycken

Source: SIAM Journal on Matrix Analysis and Applications. 45:2360-2386

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical optimization and variational techniques, Eigenvalues, singular values, and eigenvectors, eigenspaces, trace optimization, 15A69, 15A18, Methods of reduced gradient type, Diagonalization, Jordan forms, partial diagonalization, Numerical Analysis (math.NA), Grassmann manifolds, Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Numerical Analysis, invariant subspaces, Mathematics - Optimization and Control, gradient descent

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Access URL: http://arxiv.org/abs/2306.10379

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

Geodesic Convexity of the Symmetric Eigenvalue Problem and Convergence of Steepest Descent: Geodesic convexity of the symmetric eigenvalue problem and convergence of steepest descent

Authors: Foivos Alimisis Bart Vandereycken

Source: J Optim Theory Appl

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, low-rank approximation, Eigenvalues, singular values, and eigenvectors, geodesic convexity, block Rayleigh quotient, Quadratic programming, Riemannian optimization, Article, Grassmann manifold

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Access URL: https://pubmed.ncbi.nlm.nih.gov/39493644

A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains: A scalable two-level domain decomposition eigensolver for periodic Schrödinger eigenstates in anisotropically expanding domains

Authors: Lambert Theisen Benjamin Stamm

Source: SIAM Journal on Scientific Computing. 46:A3067-A3093

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, FOS: Computer and information sciences, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Iterative numerical methods for linear systems, Multigrid methods, domain decomposition for boundary value problems involving PDEs, finite element method, Schrödinger equation, 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, coarse spaces, Computational Engineering, Finance, and Science (cs.CE), domain decomposition, preconditioning, FOS: Mathematics, iterative methods, 65N25, 65F15, 65N30, 65F10, 65N22, 65N55, 65F08, Preconditioners for iterative methods, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science

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Access URL: http://arxiv.org/abs/2311.08757

Informed Normalized Gradient Flow Method for Parameterized Schrödinger Operators: A Case Study on Photonic Graphene: Informed normalized gradient flow method for parameterized Schrödinger operators: a case study on photonic graphene

Authors: Guo, Hailong Lorin, Emmanuel Noxon, Charlotte et al.

Source: Journal of Scientific Computing. 103

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Schrödinger operator, machine learning, General mathematical topics and methods in quantum theory, graphene, eigenvalue problem, neural networks, Artificial neural networks and deep learning, Atomic physics

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A Two-Level Block Preconditioned Jacobi–Davidson Method for Multiple and Clustered Eigenvalues of Elliptic Operators: A two-level block preconditioned Jacobi-Davidson method for multiple and clustered eigenvalues of elliptic operators

Authors: Qigang Liang Wei Wang Xuejun Xu

Source: SIAM Journal on Numerical Analysis. 62:998-1019

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Multigrid methods, domain decomposition for boundary value problems involving PDEs, finite element discretization, multiple and clustered eigenvalues, Rate of convergence, degree of approximation, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 01 natural sciences, PDE eigenvalue problems, preconditioned Jacobi-Davidson method, overlapping domain decomposition, FOS: Mathematics, Preconditioners for iterative methods, Mathematics - Numerical Analysis, 0101 mathematics

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Access URL: http://arxiv.org/abs/2203.06327

A method for solving ill-conditioned separable nonlinear least squares problems and its application

Authors: Wang, Luyao Liu, Guolin Chen, Yang et al.

Source: Journal of Computational and Applied Mathematics. 466:116624

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, variable projection, Ill-posedness and regularization problems in numerical linear algebra, ridge estimation, singular value decomposition, Orthogonalization in numerical linear algebra, ill-conditioned matrix, height anomaly

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Access URL: https://zbmath.org/8031358
https://doi.org/10.1016/j.cam.2025.116624

Global bounds of backward errors of polynomial eigenvalue problem solved by a companion linearization

Authors: Yang, Ziyin Wang, Zekun Cao, Zongqi et al.

Source: Computational and Applied Mathematics. 44

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, scaling, linearization, backward error, Matrix pencils, matrix polynomial

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High-relative-accuracy computations with Kac-Murdock-Szegö matrices and their generalizations

Authors: Jorge Delgado J. M. Peña

Source: Zaguán. Repositorio Digital de la Universidad de Zaragoza
Universidad de Zaragoza

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Roundoff error, Kac-Murdock-Szegö matrix, Direct numerical methods for linear systems and matrix inversion, Factorization of matrices, accurate computations

File Description: application/pdf; application/xml

Access URL: http://zaguan.unizar.es/record/153036
https://zbmath.org/8034187
https://doi.org/10.1007/s40314-025-03137-7

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

On convergence of the generalized Lanczos trust-region method for trust-region subproblems

Authors: Feng, Bo Wu, Gang

Source: Advances in Computational Mathematics. 51

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, 0211 other engineering and technologies, FOS: Mathematics, easy case, Mathematics - Numerical Analysis, 02 engineering and technology, Numerical Analysis (math.NA), generalized Lanczos trust-region (GLTR) method, Nonconvex programming, global optimization, trust-region subproblem, Krylov subspace, cubic regularization

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Access URL: http://arxiv.org/abs/2207.12674

A Block Lanczos Method for Large-Scale Quadratic Minimization Problems with Orthogonality Constraints: A block Lanczos method for large-scale quadratic minimization problems with orthogonality constraints

Authors: Feng, Bo Wu, Gang

Source: SIAM Journal on Scientific Computing. 46:A884-A905

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Large-scale problems in mathematical programming, Iterative numerical methods for linear systems, 0211 other engineering and technologies, 02 engineering and technology, Numerical Analysis (math.NA), Quadratic programming, block Krylov subspace, Nonconvex programming, global optimization, 01 natural sciences, quadratic minimization problems with orthogonality constraints, Numerical mathematical programming methods, QMPO, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, block Lanczos

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Access URL: http://arxiv.org/abs/2304.11886
https://zbmath.org/7820565
https://doi.org/10.1137/23m1568545