Recursive blocked algorithms for solving periodic triangular Sylvester-type matrix equations

Authors:
Robert Granat;Isak Jonsson;Bo Kågström
Affiliations:
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden;Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden;Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden
Venue:
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Year:
2006

Citing 5
Cited 1

LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs

ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]

Communications of the ACM
Recursive blocked algorithms for solving triangular systems—Part I: one-sided and coupled Sylvester-type matrix equations

ACM Transactions on Mathematical Software (TOMS)
Recursive blocked algorithms for solving triangular systems—Part II: two-sided and generalized Sylvester and Lyapunov matrix equations

ACM Transactions on Mathematical Software (TOMS)
Direct Eigenvalue Reordering in a Product of Matrices in Periodic Schur Form

SIAM Journal on Matrix Analysis and Applications

Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix Equations

Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Recently, recursive blocked algorithms for solving triangular one-sided and two-sided Sylvester-type equations were introduced by Jonsson and Kågström. This elegant yet simple technique enables an automatic variable blocking that has the potential of matching the memory hierarchies of today's HPC systems. The main parts of the computations are performed as level 3 general matrix multiply and add (GEMM) operations. We extend and apply the recursive blocking technique to solving periodic Sylvester-type matrix equations. Successive recursive splittings are performed on 3-dimensional arrays, where the third dimension represents the periodicity of a matrix equation.