Avoiding Communication in Nonsymmetric Lanczos-Based Krylov Subspace Methods

DOI10.1137/120881191zbMath1281.65057OpenAlexW2041792040MaRDI QIDQ2870667

Nicholas Knight, Erin Claire Carson, James W. Demmel

Publication date: 21 January 2014

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/120881191

zbMATH Keywords

algorithmconvergencenumerical exampleseigenvalue problemparallel computationiterative methodssparse matrixKrylov subspace methodsBICGSTABminimizing communicationBICGlarge, sparse systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05)

Related Items (10)

The non-symmetric \(s\)-step Lanczos algorithm: derivation of efficient recurrences and synchronization-reducing variants of BiCG and QMR ⋮ The Adaptive $s$-Step Conjugate Gradient Method ⋮ Analyzing the Effect of Local Rounding Error Propagation on the Maximal Attainable Accuracy of the Pipelined Conjugate Gradient Method ⋮ Avoiding Communication in Primal and Dual Block Coordinate Descent Methods ⋮ Communication lower bounds and optimal algorithms for numerical linear algebra ⋮ s-Step Enlarged Krylov Subspace Conjugate Gradient Methods ⋮ Revisiting performance of biCGStab methods for solving systems with multiple right-hand sides ⋮ Scalable Linear Solvers Based on Enlarged Krylov Subspaces with Dynamic Reduction of Search Directions ⋮ Communication Avoiding ILU0 Preconditioner ⋮ Accuracy of the $s$-Step Lanczos Method for the Symmetric Eigenproblem in Finite Precision

Uses Software

• SparseMatrix

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