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Recent Advances in Operator Theory and its Applications pp 233–252Cite as

Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 160))

Abstract

In this paper fast algorithms for the solution of systems Tu = b with a strongly nonsingular hermitian Toeplitz coefficient matrix T via different kinds of factorizations of the matrix T are discussed. The first aim is to show that ZW-factorization of T is more efficient than the corresponding LU-factorization. The second aim is to design and compare different Schurtype algorithms for LU- and ZW-factorization of T. This concerns the classical Schur-Bareiss algorithm, 3-term one-step and double-step algorithms, and the Schur-type analogue of a Levinson-type algorithm of B. Krishna and H. Krishna. The latter one reduces the number of the multiplications by almost 50% compared with the classical Schur-Bareiss algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, P.O.Box 5969, Safat, 1306, Kuwait

    Georg Heinig

  2. Department of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany

    Karla Rost

Authors
  1. Georg Heinig
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  2. Karla Rost
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel

    Israel Gohberg

  2. Beer-Sheva

    D. Alpay  & P. A. Fuhrmann  & 

  3. Haifa

    J. Arazy  & L. E. Lerer  & 

  4. Tel Aviv

    A. Atzmon  & A. Ben-Artzi  & 

  5. Blacksburg

    J. A. Ball

  6. Bloomington

    H. Bercovici

  7. Chemnitz

    A. Böttcher  & G. Heinig  & 

  8. Athens, USA

    K. Clancey

  9. Buffalo

    L. A. Coburn

  10. Waterloo, Ontario

    K. R. Davidson

  11. College Station

    R. G. Douglas

  12. Groningen

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  13. Rehovot

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  14. Mainz

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  15. La Jolla

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  16. Amsterdam

    M. A. Kaashoek

  17. Argonne

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  18. Tokyo

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  19. Calgary

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  27. Leiden

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  28. Santa Cruz

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  30. Rennes

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  31. Department of Mathematics, FEW Vrije Universiteit, De Boelelaan 1081A, 1081 HV, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  32. Dipartimento di Matematica, Università di Cagliari, Viale Merello 92, 09123, Cagliari, Italy

    Sebastiano Seatzu  & Cornelis van der Mee  & 

Additional information

Dedicated to our teacher and friend Israel Gohberg

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Heinig, G., Rost, K. (2005). Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization. In: Gohberg, I., et al. Recent Advances in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 160. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7398-9_11

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