A parallel preconditioned conjugate gradient package for solving sparse linear systems on a Cray Y-MP

DOI10.1016/0168-9274(91)90045-2zbMath0738.65025OpenAlexW2076485756MaRDI QIDQ1181505

Michael A. Heroux, Chao Yang, Phuong Anh Vu

Publication date: 27 June 1992

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(91)90045-2

zbMATH Keywords

parallel computingsparse matrixscalingpackagecomputational resultsmatrix-vector productincomplete Choleskyshared-memoryCRAY Y-MPvector/parallel computers\(LU\) factorizationsCRAY PCGpreconditioned conjugate gradient iterative methods

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Software, source code, etc. for problems pertaining to linear algebra (15-04)

Related Items

A PETSc-based parallel implementation of finite element method for elasticity problems ⋮ Efficient approximate solution of sparse linear systems ⋮ Parallel preconditioned conjugate-gradient type algorithms for general sparsity structures ⋮ A comparison of FAC and PCG methods for solving composite grid problems ⋮ Numerical experiments with two approximate inverse preconditioners ⋮ Fine-Grained Parallel Incomplete LU Factorization

Uses Software

• NSPCG
• ITSOL
• SPARSKIT
• CGS
• Harwell-Boeing sparse matrix collection

Cites Work

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• A new storage scheme for an efficient implementation of the sparse matrix-vector product
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• Data structures to vectorize CG algorithms for general sparsity patterns
• Practical use of the conjugate gradient method on parallel supercomputers
• SPARSE MATRIX MULTIPLICATION ON VECTOR COMPUTERS
• Krylov Subspace Methods on Supercomputers
• Conjugate Gradient-Like Algorithms for Solving Nonsymmetric Linear Systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
• On Vectorizing Incomplete Factorization and SSOR Preconditioners
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Sparse matrix test problems
• An Incomplete Factorization Technique for Positive Definite Linear Systems
• The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”
• Methods of conjugate gradients for solving linear systems

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