Research Article

Solving the block–Toeplitz least-squares problem in parallel

  1. P. Alonso1,*,
  2. J. M. Badía2,
  3. A. M. Vidal1

Article first published online: 29 NOV 2004

DOI: 10.1002/cpe.883

Issue

Concurrency and Computation: Practice and Experience

Concurrency and Computation: Practice and Experience

Volume 17, Issue 1, pages 49–67, January 2005

Additional Information

How to Cite

Alonso, P., Badía, J. M. and Vidal, A. M. (2005), Solving the block–Toeplitz least-squares problem in parallel. Concurrency Computat.: Pract. Exper., 17: 49–67. doi: 10.1002/cpe.883

Author Information

  1. 1

    Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, 46071 Valencia, Spain

  2. 2

    Departamento de Ingenierá y Ciencia de los Computadores, Universidad Jaume I, 12080 Castellón, Spain

*Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, 46071 Valencia, Spain

Publication History

  1. Issue published online: 29 NOV 2004
  2. Article first published online: 29 NOV 2004
  3. Manuscript Accepted: 14 JAN 2004
  4. Manuscript Revised: 28 OCT 2003
  5. Manuscript Received: 29 OCT 2002

Funded by

  • Ministerio de Educación, Cultura y Deporte, Spain. Grant Number: CICYT TIC 2000-1683-C03-03

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Keywords:

  • least-squares problem;
  • block–Toeplitz matrices;
  • Toeplitz–block matrices;
  • displacement structure;
  • Generalized Schur Algorithm;
  • parallel algorithms;
  • clusters of personal computers

Abstract

In this paper we present two versions of a parallel algorithm to solve the block–Toeplitz least-squares problem on distributed-memory architectures. We derive a parallel algorithm based on the seminormal equations arising from the triangular decomposition of the product TTT. Our parallel algorithm exploits the displacement structure of the Toeplitz-like matrices using the Generalized Schur Algorithm to obtain the solution in O(mn) flops instead of O(mn2) flops of the algorithms for non-structured matrices. The strong regularity of the previous product of matrices and an appropriate computation of the hyperbolic rotations improve the stability of the algorithms. We have reduced the communication cost of previous versions, and have also reduced the memory access cost by appropriately arranging the elements of the matrices. Furthermore, the second version of the algorithm has a very low spatial cost, because it does not store the triangular factor of the decomposition. The experimental results show a good scalability of the parallel algorithm on two different clusters of personal computers. Copyright © 2005 John Wiley & Sons, Ltd.

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