On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method

DOI10.1002/nla.1680010503zbMath0838.65031OpenAlexW2059363444MaRDI QIDQ4868092

James S. Otto, Thomas A. Manteuffel

Publication date: 3 June 1996

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.1680010503

zbMATH Keywords

orthogonal polynomialsfield of valuespreconditioned conjugate gradient iterationresidual polynomialsgeneralized Ritz valuespseudo-Ritz values

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

A note on the convergence behavior of GMRES, Harmonic projection methods for large non-symmetric eigenvalue problems, Ritz and pseudo-Ritz values using matrix polynomials, Unnamed Item, On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method, Eigenvalue inclusion regions from inverses of shifted matrices, The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors, Convergence properties of block GMRES and matrix polynomials, Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm, Analysis of acceleration strategies for restarted minimal residual methods, On the use of harmonic Ritz pairs in approximating internal eigenpairs

Uses Software

• CHEBYCODE

Cites Work

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• On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
• Minimax Polynomial Preconditioning for Hermitian Linear Systems
• On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method
• Methods of conjugate gradients for solving linear systems