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O(n) Algorithms for Banded Plus Semiseparable Matrices

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Numerical Methods for Structured Matrices and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 199))

Abstract

We present a new representation for the inverse of a matrix that is a sum of a banded matrix and a semiseparable matrix. In particular, we show that under certain conditions, the inverse of a banded plus semiseparable matrix can also be expressed as a banded plus semiseparable matrix. Using this result, we devise a fast algorithm for the solution of linear systems of equations involving such matrices. Numerical results show that the new algorithm competes favorably with existing techniques in terms of computational time.

This work was done when the authors were at Purdue University.

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Author information

Authors and Affiliations

  1. Intel Corporation, Hillsboro, OR, 97124, USA

    Jitesh Jain

  2. Synopsys Inc., Mountain View, CA, 94043, USA

    Hong Li

  3. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907-1285, USA

    Cheng-Kok Koh & Venkataramanan Balakrishnan

Authors
  1. Jitesh Jain
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  2. Hong Li
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  3. Cheng-Kok Koh
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  4. Venkataramanan Balakrishnan
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, UniversitĂ  di Pisa, Largo Bruno Pontecorvo, 5, 56127, Pisa, Italy

    Dario Andrea Bini

  2. Institut für Mathematik, Technische Universität Berlin, Straβe des 17. Juni 136, 10623, Berlin, Germany

    Volker Mehrmann

  3. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  4. Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina Street, 8, Moscow, 119991, Russia

    Eugene E. Tyrtyshnikov

  5. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001, Leuven (Heverlee), Belgium

    Marc van Barel

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© 2010 Birkhäuser Verlag Basel/Switzerland

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Jain, J., Li, H., Koh, CK., Balakrishnan, V. (2010). O(n) Algorithms for Banded Plus Semiseparable Matrices. In: Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E.E., van Barel, M. (eds) Numerical Methods for Structured Matrices and Applications. Operator Theory: Advances and Applications, vol 199. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8996-3_15

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