Explicitly preconditioned conjugate gradient method for the solution of unsymmetric linear systems

DOI10.1080/00207169208804103zbMath0758.65027OpenAlexW2134482604MaRDI QIDQ4021065

Igor E. Kaporin

Publication date: 17 January 1993

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207169208804103

zbMATH Keywords

parallel computationtracecondition numberdeterminantparallel computersoptimal convergencenonsymmetric systemspreconditioned conjugate gradient methodssymmetric positive definite linear systemsincomplete inverse Cholesky decomposition

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Parallel numerical computation (65Y05)

Related Items (5)

Triangular skew-symmetric iterative solvers for strongly nonsymmetric positive real linear system of equations ⋮ Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations ⋮ A power sparse approximate inverse preconditioning procedure for large sparse linear systems ⋮ Iterative algorithm for minimal norm least squares solution to general linear matrix equations ⋮ Gradient-based maximal convergence rate iterative method for solving linear matrix equations

Uses Software

• CGS

Cites Work

• Unnamed Item
• Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems
• Preconditioning techniques for nonsymmetric and indefinite linear systems
• A projection method for solving nonsymmetric linear systems on multiprocessors
• Iterative solution methods for certain sparse linear systems with a non- symmetric matrix arising from PDE-problems
• Domain decomposition for parallel row projection algorithms
• A class of iterative methods for finite element equations
• Scaling of matrices to achieve specified row and column sums
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Development of Parallel Methods for a $1024$-Processor Hypercube
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices

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