Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights

DOI10.1007/BF02145581zbMath0752.65010MaRDI QIDQ1186620

Gene H. Golub, Daniel L. Boley, Martin H. Gutknecht, Sylvan Elhay

Publication date: 28 June 1992

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

orthogonal polynomialsnumerical exampleserror correctionmatrix factorizationChebyshev algorithmbased fault tolerancenonsymmetric matrix Lanczos process

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20) Reliability, testing and fault tolerance of networks and computer systems (68M15)

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Construction of polynomials that are orthogonal with respect to a discrete bilinear form, VPAStab\((J,L)\): an iterative method with look-ahead for the solution of large sparse linear systems, A linear system solver based on a modified Krylov subspace method for breakdown recovery, On moments based Padé approximations of ruin probabilities, Avoiding breakdown in the CGS algorithm, Avoiding breakdown and near-breakdown in Lanczos type algorithms, Breakdowns in the implementation of the Lánczos method for solving linear systems, The Lanczos algorithm and Hankel matrix factorization, A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms, Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem, Lanczos-type algorithms for solving systems of linear equations, Krylov space methods on state-space control models

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