Search Results - numerical computation of eigenvalues and eigenvectors

On the Numerical Computation of Eigenvalues and Eigenvectors of Symmetric Integral Equations

Authors: Linz, Peter

Source: Mathematics of Computation, 1970 Oct 01. 24(112), 905-910.

Access URL: https://www.jstor.org/stable/2004624

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

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

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 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

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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

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

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

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

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

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

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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

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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FAST AND BACKWARD STABLE COMPUTATION OF EIGENVALUES AND EIGENVECTORS OF MATRIX POLYNOMIALS

Authors: AURENTZ, JARED MACH, THOMAS ROBOL, LEONARDO et al.

Source: Mathematics of Computation, 2019 Jan 01. 88(315), 313-347.

Access URL: https://www.jstor.org/stable/90025037

Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems

Authors: Desong Kong Jie Shen Li-Lian Wang et al.

Source: Advances in Computational Mathematics. 50

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Asymptotic distributions of eigenvalues in context of PDEs, eigenvalue distributions, spectral method in time, QZ decomposition, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, matrix diagonalisation, 01 natural sciences, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), KdV equations (Korteweg-de Vries equations), Bessel and generalised Bessel polynomials, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, 65M70, 65L15, 65F15, 33C45, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Mathematics - Numerical Analysis, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Legendre dual Petrov-Galerkin methods

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Access URL: http://arxiv.org/abs/2211.10599
https://zbmath.org/7932062
https://doi.org/10.1007/s10444-024-10190-z

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

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

Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors: Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors.

Authors: Roger C. E. Tan Alan L. Andrew MATHEMATICS et al.

Contributors: Roger C. E. Tan Alan L. Andrew MATHEMATICS et al.

Source: Numerical Linear Algebra with Applications. 7:151-167

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, 010301 Numerical Analysis, algorithm, Multiple eigenvalues, numerical results, simultaneous iteration, eigenvalue and eigenvector sensitivities, Eigenvalue and eigenvector sensitivities, Simultaneous iteration, Close eigenvalues, convergence acceleration, 230116 Numerical Analysis, multiple eigenvalues, close eigenvalues

File Description: application/xml

Access URL: https://zbmath.org/2098215
https://doi.org/10.1002/1099-1506(200005)7:4<151::aid-nla191>3.0.co;2-m
https://link.springer.com/chapter/10.1007%2F978-3-0348-8181-4_6
https://rd.springer.com/chapter/10.1007/978-3-0348-8181-4_6
https://onlinelibrary.wiley.com/doi/abs/10.1002/1099-1506%28200005%297%3A4%3C151%3A%3AAID-NLA191%3E3.0.CO%3B2-M
https://dblp.uni-trier.de/db/journals/nla/nla7.html#AndrewT00

Computation of Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors of Symmetric Matrix Pencils: Computation of derivatives of repeated eigenvalues and the corresponding eigenvectors of symmetric matrix pencils

Authors: Andrew, A.L. Tan, R.C.E. MATHEMATICS

Contributors: Andrew, A.L. Tan, R.C.E. MATHEMATICS

Source: SIAM Journal on Matrix Analysis and Applications. 20:78-100

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Multiple eigenvalues, 4. Education, numerical results, algorithms, symmetric matrix pencils, 01 natural sciences, numerical stability, eigenvalue and eigenvector sensitivities, Eigenvalue and eigenvector sensitivities, derivatives, Close eigenvalues, multiple eigenvalues, 0101 mathematics, Matrix pencils, close eigenvalues

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Access URL: https://zbmath.org/1288437
https://doi.org/10.1137/s0895479896304332
https://epubs.siam.org/doi/10.1137/S0895479896304332
https://dblp.uni-trier.de/db/journals/siammax/siammax20.html#AndrewT98
https://dialnet.unirioja.es/servlet/articulo?codigo=2848859