Data structures to vectorize CG algorithms for general sparsity patterns

DOI10.1007/BF01932741zbMath0685.65022MaRDI QIDQ1262077

Giuseppe Radicati di Brozolo, Gaia Valeria Paolini

Publication date: 1989

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

performanceimplementationdata structurevector processorconjugate gradient-type iterative algorithmsILU type preconditionerssparse computational kernelssparse triangular systemswavefront approach

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Parallel numerical computation (65Y05) Theory of operating systems (68N25)

Related Items (2)

Parallel preconditioned conjugate-gradient type algorithms for general sparsity structures ⋮ A parallel preconditioned conjugate gradient package for solving sparse linear systems on a Cray Y-MP

Uses Software

• CGS
• Harwell-Boeing sparse matrix collection

Cites Work

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• The block preconditioned conjugate gradient method on vector computers
• A survey of preconditioned iterative methods for linear systems of algebraic equations
• The performance of FORTRAN implementations for preconditioned conjugate gradients on vector computers
• Approximating the inverse of a matrix for use in iterative algorithms on vector processors
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems
• Matrix multiplication by diagonals on a vector/parallel processor
• The effect of ordering on preconditioned conjugate gradients
• ICCG and related methods for 3D problems on vector computers
• Block Preconditioning for the Conjugate Gradient Method
• Implementation of the GMRES Method Using Householder Transformations
• Polynomial Preconditioners for Conjugate Gradient Calculations
• 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
• Conjugate-gradient subroutines for the IBM 3090 Vector Facility
• An Incomplete Factorization Technique for Positive Definite Linear Systems
• The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
• A Vectorizable Variant of some ICCG Methods
• 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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