A normalized implicit conjugate gradient method for the solution of large sparse systems of linear equations

DOI10.1016/0045-7825(80)90075-4zbMath0447.65011OpenAlexW2076339437MaRDI QIDQ1146495

David J. Evans, Elias A. Lipitakis

Publication date: 1980

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(80)90075-4

zbMATH Keywords

examplesgeneralized conjugate gradient methodincomplete factorizationsymmetric, positive definite, pentadiagonal matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (16)

Approximate root-free factorization techniques for solving elliptic difference equations in three space variables ⋮ Explicit preconditioned iterative methods for solving large unsymmetric finite element systems ⋮ A class of explicit preconditioned conjugate gradient methods for solving large finite element systems ⋮ Normalized factorization procedures for the solution of self-adjoint elliptic partial differential equations in three-space dimensions ⋮ Solving non-linear elliptic difference equations by extendable sparse factorization procedures ⋮ Normalized implicit methods for the solution of non-linear elliptic boundary value problems ⋮ Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods ⋮ ON THE RATE OF CONVERGENCE AND COMPLEXITY OF NORMALIZED IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES ⋮ A performance study of normalized explicit finite element approximate inverse preconditioning on uniprocessor and multicomputer systems ⋮ Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors ⋮ On sparse and compact preconditioned conjugate gradient methods for partial differential equations ⋮ Implicit semi-direct methods based on root-free sparse factorization procedures ⋮ A normalized sparse linear equations solver ⋮ Solving linear finite element systems by normalized approximate matrix factorization semi-direct methods ⋮ Generalized extended to the limit sparse factorization techniques for solving unsymmetric finite element systems ⋮ The use of second degree normalized implicit conjugate gradient methods for solving large sparse systems of linear equations

Cites Work

• A normalised algorithm for the solution of symmetric general five-term linear systems of semi-bandwidth M
• A Method of Normalized Block Iteration
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• A class of first order factorization methods
• Methods of conjugate gradients for solving linear systems
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