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Accurate Computations for Some Classes of Matrices

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Numerical Mathematics and Advanced Applications - ENUMATH 2013

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

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Abstract

A square matrix is called a P-matrix if all its principal minors are positive. Subclasses of P-matrices with many applications are the nonsingular totally positive matrices and the nonsingular M-matrices. For diagonally dominant M-matrices and some subclasses of nonsingular totally nonnegative matrices, accurate methods for computing their singular values, eigenvalues or inverses have been obtained, assuming that adequate natural parameters are provided. The adequate parameters for diagonally dominant M-matrices are the row sums and the off-diagonal entries, and for nonsingular totally nonnegative matrices are the entries of their bidiagonal factorization. In this paper we survey some recent extensions of these methods to other related classes of matrices.

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Author information

Authors and Affiliations

  1. Dpto. de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

    Juan M. Peña

Authors
  1. Juan M. Peña
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Correspondence to Juan M. Peña .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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Peña, J.M. (2015). Accurate Computations for Some Classes of Matrices. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_32

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