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Specialized Spectral Division Algorithms for Generalized Eigenproblems Via the Inverse-Free Iteration

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Book cover Applied Parallel Computing. State of the Art in Scientific Computing (PARA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4699))

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Abstract

We present two implementations of the inverse-free iteration for spectral division that reduce the computational cost of the traditional algorithm. One of the implementations is mainly composed of efficient BLAS-3 operations, and can be employed for spectral division of large-scale generalized eigenproblems on current computer architectures.

This research was partially supported by the DAAD programme Acciones Integradas HA2005-0081, the CICYT project TIN2005-09037-C02-02 and FEDER, and project No. P1B-2004-6 of the Fundación Caixa-Castellón/Bancaixa and UJI.

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References

  1. Antoulas, A.C.: Approximation of Large-Scale Dynamical Systems. SIAM Publications, Philadelphia (2005)

    MATH  Google Scholar 

  2. Bai, Z., Demmel, J., Gu, M.: An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems. Numer. Math. 76(3), 279–308 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Benner, P.: Contributions to the Numerical Solution of Algebraic Riccati Equations and Related Eigenvalue Problems. Logos–Verlag, Germany (1997)

    MATH  Google Scholar 

  4. Braman, K., Byers, R., Mathias, R.: The multishift QR algorithm. Part I: Maintaining well-focused shifts and level 3 performance. SIAM J. Matrix Anal. Appl. 23(4), 929–947 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Braman, K., Byers, R., Mathias, R.: The multishift QR algorithm. SIAM J. Matrix Anal. Appl. 23(4), 948–973 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kågström, B., Kressner, D.: Multishift variants of the QZ algorithm with aggressive early deflation. SIAM J. Matrix Anal. Appl. 29(1), 199–227 (2006)

    Article  MathSciNet  Google Scholar 

  7. Malyshev, A.N.: Parallel algorithm for solving some spectral problems of linear algebra. Linear Algebra Appl. 188/189, 489–520 (1993)

    Article  MathSciNet  Google Scholar 

  8. Moler, C.B., Stewart, G.W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10, 241–256 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  9. Roberts, J.D.: Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. Internat. J. Control 32, 677–687 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sima, V.: Algorithms for Linear-Quadratic Optimization, Pure and Applied Mathematics, vol. 200. Marcel Dekker, Inc., New York (1996)

    Google Scholar 

  11. Sun, X., Quintana-Ortí, E.S.: The generalized Newton iteration for the matrix sign function. SIAM J. Sci. Comput. 24(2), 669–683 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sun, X., Quintana-Ortí, E.S.: Spectral division methods for block generalized Schur decompositions. Math. Comp. 73, 1827–1847 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Depto. de Ingeniería y Ciencia de Computadores, Universidad Jaume I, 12.071–Castellón, Spain

    Mercedes Marqués, Enrique S. Quintana-Ortí & Gregorio Quintana-Ortí

Authors
  1. Mercedes Marqués
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  2. Enrique S. Quintana-Ortí
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  3. Gregorio Quintana-Ortí
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Bo Kågström Erik Elmroth Jack Dongarra Jerzy Waśniewski

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Marqués, M., Quintana-Ortí, E.S., Quintana-Ortí, G. (2007). Specialized Spectral Division Algorithms for Generalized Eigenproblems Via the Inverse-Free Iteration. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2006. Lecture Notes in Computer Science, vol 4699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75755-9_19

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  • DOI: https://doi.org/10.1007/978-3-540-75755-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75754-2

  • Online ISBN: 978-3-540-75755-9

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