Evaluation of matrix functions with the block Lanczos algorithm

DOI10.1016/S0898-1221(96)00218-0zbMath0869.65027MaRDI QIDQ678426

C. Cabos

Publication date: 1 September 1997

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

numerical exampleeigenvalueseigenvectorserror boundsforced vibrationmatrix polynomialmatrix functionsblock Lanczos iterationRitz vectors

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Forced motions in linear vibration theory (70J35)

Cites Work

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• An iterative solution method for solving \(f(A)x=b\), using Krylov subspace information obtained for the symmetric positive definite matrix A
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Some new characterizations of the Chebyshev polynomials
• How to Implement the Spectral Transformation
• The Advantages of Inverted Operators in Rayleigh–Ritz Approximations
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• The simultaneous computation of a few of the algebraically largest and smallest eigenvalues of a large, sparse, symmetric matrix
• Error Bounds for Dynamic Responses in Forced Vibration Problems
• Two polynomial methods of calculating functions of symmetric matrices

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