On a class of Chebyshev approximation problems which arise in connection with a conjugate gradient type method

DOI10.1007/BF01389449zbMath0611.65016OpenAlexW2008848819MaRDI QIDQ1087307

Stephan Ruscheweyh, Roland W. Freund

Publication date: 1986

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133085

zbMATH Keywords

conjugate gradient methodNumerical examplesChebyshev approximationoptimal semi-iterative method

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Iterative numerical methods for linear systems (65F10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (15)

Iterative k-step methods for computing possibly repulsive fixed points in Banach spaces ⋮ On some approximation problems for complex polynomials ⋮ Explicit generalized Zolotarev polynomials with complex coefficients ⋮ The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems ⋮ A dual-type problem to Christoffel function ⋮ The growth of polynomials outside of a compact set-the Bernstein-Walsh inequality revisited ⋮ On Non-Hermitian Positive (Semi)Definite Linear Algebraic Systems Arising from Dissipative Hamiltonian DAEs ⋮ Asymptotics of Chebyshev polynomials. V: Residual polynomials ⋮ On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices ⋮ An Iteration for Indefinite Systems and Its Application to the Navier--Stokes Equations ⋮ Extremal problems of Chebyshev type ⋮ Polynomial approximation of functions of matrices and applications ⋮ A complex extremal problem of Chebyshev type ⋮ Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra ⋮ On the constrained Chebyshev approximation problem on ellipses

Cites Work

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• Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II
• Richardson's iteration for nonsymmetric matrices
• The analysis of k-step iterative methods for linear systems from summability theory
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• A Unified Approach to Certain Problems of Approximation and Minimization
• Some Inequalities for Polynomials
• A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations

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