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V-cycle Optimal Convergence for DCT-III 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

The paper analyzes a two-grid and a multigrid method for matrices belonging to the DCT-III algebra and generated by a polynomial symbol. The aim is to prove that the convergence rate of the considered multigrid method (V-cycle) is constant independent of the size of the given matrix. Numerical examples from differential and integral equations are considered to illustrate the claimed convergence properties.

The work of the author was partially supported by MIUR, grant number 2006017542.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via Cozzi 53, I-20125, Milano, Italy

    C. Tablino Possio

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  1. C. Tablino Possio
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università 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

Additional information

Dedicated to Georg Heinig

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© 2010 Birkhäuser Verlag Basel/Switzerland

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Tablino Possio, C. (2010). V-cycle Optimal Convergence for DCT-III 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_17

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