An optimum iterative method for solving any linear system with a square matrix

DOI10.1007/BF01934703zbMath0636.65025MaRDI QIDQ1098228

Dennis C. Smolarski, Paul E. Saylor

Publication date: 1988

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

Chebyshev methodleast squaresRichardson iterationManteuffel algorithmnonsymmetric matriceslocation of the eigenvaluesnonhermitian matricesoptimal Chebyshev choiceoptimum iteration parameters

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (13)

Polynomial Preconditioned GMRES and GMRES-DR ⋮ A polynomial preconditioner for the GMRES algorithm ⋮ Locally optimal and heavy ball GMRES methods ⋮ Parallel computation of polynomials with minimal uniform norm and its application to large eigenproblems ⋮ On semiiterative methods generated by Faber polynomials ⋮ The use of the CADNA library for validating the numerical results of the hybrid GMRES algorithm ⋮ Quasi-kernel polynomials and their use in non-Hermitian matrix iterations ⋮ An adaptive method for solving nonsymmetric linear systems involving applications of SCPACK ⋮ Synthesis of fast and superfast solvers of large systems of linear algebraic equations using control theory methods ⋮ Leja, Fejér-Leja and \(\mathfrak{R}\)-Leja sequences for Richardson iteration ⋮ The application of Leja points to Richardson iteration and polynomial preconditioning ⋮ Implementation of an adaptive algorithm for Richardson's method ⋮ Experiments with Krylov subspace methods on a massively parallel computer

Uses Software

• CHEBYCODE

Cites Work

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• Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
• Extremal Polynomials with Application to Richardson Iteration for Indefinite Linear Systems
• On Generating Orthogonal Polynomials
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• A class of first order factorization methods
• A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations
• Calculation of Gauss Quadrature Rules

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