Article

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

Authors:

Bo KågströmAuthors Info & Claims

PARA'06: Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing

Pages 531 - 539

Published: 18 June 2006 Publication History

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.

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Cited By

Huang BMa C(2019)Finite iterative algorithm for the symmetric periodic least squares solutions of a class of periodic Sylvester matrix equationsNumerical Algorithms10.1007/s11075-018-0553-881:1(377-406)Online publication date: 21-May-2019
https://dl.acm.org/doi/10.1007/s11075-018-0553-8
Hajarian M(2018)A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix EquationsCircuits, Systems, and Signal Processing10.1007/s00034-014-9842-134:1(105-125)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1007/s00034-014-9842-1
Hajarian M(2017)Convergence analysis of generalized conjugate direction method to solve general coupled Sylvester discrete-time periodic matrix equationsInternational Journal of Adaptive Control and Signal Processing10.5555/3193602.319360531:7(985-1002)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.5555/3193602.3193605
Show More Cited By

Index Terms

Recursive blocked algorithms for solving periodic triangular Sylvester-type matrix equations
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Guide Proceedings

PARA'06: Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing

June 2006

1191 pages

ISBN:3540757546

Editors:
Bo Kågström
Umeå University, Department of Computing Science and High Performance Computing Center North, Umeå, Sweden
,
Erik Elmroth
Umeå University, Department of Computing Science and High Performance Computing Center North, Umeå, Sweden
,
Jack Dongarra
University of Tennessee, Department of Computer Science, Knoxville, TN
,
Jerzy Waśniewski
Technical University of Denmark, Informatics and Mathematical Modelling, Lyngby, Denmark

Sponsors

Umeå University
VR: The Swedish Research Council

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 18 June 2006

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Cited By

Huang BMa C(2019)Finite iterative algorithm for the symmetric periodic least squares solutions of a class of periodic Sylvester matrix equationsNumerical Algorithms10.1007/s11075-018-0553-881:1(377-406)Online publication date: 21-May-2019
https://dl.acm.org/doi/10.1007/s11075-018-0553-8
Hajarian M(2018)A Finite Iterative Method for Solving the General Coupled Discrete-Time Periodic Matrix EquationsCircuits, Systems, and Signal Processing10.1007/s00034-014-9842-134:1(105-125)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1007/s00034-014-9842-1
Hajarian M(2017)Convergence analysis of generalized conjugate direction method to solve general coupled Sylvester discrete-time periodic matrix equationsInternational Journal of Adaptive Control and Signal Processing10.5555/3193602.319360531:7(985-1002)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.5555/3193602.3193605
Andersson PGranat RJonsson IKågström B(2008)Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix EquationsProceedings of the 14th international Euro-Par conference on Parallel Processing10.1007/978-3-540-85451-7_83(780-789)Online publication date: 26-Aug-2008
https://dl.acm.org/doi/10.1007/978-3-540-85451-7_83

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