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Block Variants of the COCG and COCR Methods for Solving Complex Symmetric Linear Systems with Multiple Right-Hand Sides

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Numerical Mathematics and Advanced Applications ENUMATH 2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 112))

Abstract

In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symmetric linear systems with multiple right hand sides. The proposed Block iterative solvers can fully exploit the complex symmetry property of coefficient matrix of the linear system. We report on extensive numerical experiments to show the favourable convergence properties of our newly developed Block algorithms for solving realistic electromagnetic simulations.

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Notes

  1. 1.

    For our practical implementation, we use MATLAB qr-function “qr(W,0)” for a given matrix \(W \in \mathbb{C}^{n\times p}\).

  2. 2.

    http://math.nist.gov/MatrixMarket/matrices.html

  3. 3.

    https://github.com/Hsien-Ming-Ku/Test_matrices/tree/master/Example2

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Xian-Ming Gu & Ting-Zhu Huang

  2. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Nijenborgh 9, 407, 9700, AK Groningen, The Netherlands

    Xian-Ming Gu

  3. School of Science and Technology, Nottingham Trent University, Clifton Campus, Nottingham, NG11 8NS, UK

    Bruno Carpentieri

  4. School of Mathematics and Statistics, Taishan University, Taian, 271021, China

    Jing Meng

Authors
  1. Xian-Ming Gu
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  2. Bruno Carpentieri
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  3. Ting-Zhu Huang
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  4. Jing Meng
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Corresponding author

Correspondence to Bruno Carpentieri .

Editor information

Editors and Affiliations

  1. Mathematics & Applied Mathematics, Middle East Technical University Mathematics & Applied Mathematics, Ankara, Turkey

    Bülent Karasözen

  2. Dept of Computer Engg, Middle East Technical Univ Dept of Computer Engg, Cankaya, Ankara, Turkey

    Murat Manguoğlu

  3. Middle East Technical University Mathematics & Institute of Applied Mathe, Ankara, Turkey

    Münevver Tezer-Sezgin

  4. Civil Engineering & Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Serdar Göktepe

  5. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Turkey

    Ömür Uğur

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Gu, XM., Carpentieri, B., Huang, TZ., Meng, J. (2016). Block Variants of the COCG and COCR Methods for Solving Complex Symmetric Linear Systems with Multiple Right-Hand Sides. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_30

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