Convergence and instability in PCG methods for bordered systems

DOI10.1016/0898-1221(95)00177-ZzbMath0835.65096OpenAlexW1984965528MaRDI QIDQ1905916

G. L. Kraut, Ian Gladwell

Publication date: 22 January 1996

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(95)00177-z

zbMATH Keywords

convergencefinite differencestwo-point boundary value problemmatrix splittingpreconditioned conjugate gradient methodspline collocationmultiple shootingbordered almost block diagonal systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (1)

Almost block diagonal linear systems: sequential and parallel solution techniques, and applications

Uses Software

• NAG
• nag

Cites Work

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• General framework, stability and error analysis for numerical stiff boundary value methods
• Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
• Comparison of splittings used with the conjugate gradient algorithm
• A Taxonomy for Conjugate Gradient Methods
• Stable Parallel Algorithms for Two-Point Boundary Value Problems
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
• A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable

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