ON THE RATE OF CONVERGENCE AND COMPLEXITY OF NORMALIZED IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES

DOI10.1142/S0219876204000174zbMath1083.65102OpenAlexW1966704369MaRDI QIDQ5695060

George A. Gravvanis, Konstantinos M. Giannoutakis

Publication date: 11 October 2005

Published in: International Journal of Computational Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219876204000174

zbMATH Keywords

computational complexityrate of convergencenumerical resultselliptic boundary value problemsconjugate gradient-type methodsimplicit preconditioning methodsfinite difference discretization methodapproximate sparse factorization proceduresparse symmetric positive definite diagonally dominant matrixself-adjoint partial differential equation

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite difference methods for boundary value problems involving PDEs (65N06) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (1)

A Distributed Normalized Explicit Preconditioned Conjugate Gradient Method

Cites Work

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• On the convergence rate of the conjugate gradients in presence of rounding errors
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• New convergence results and preconditioning strategies for the conjugate gradient method

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