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Accurate Computations for Some Classes of Matrices

  • Juan M. Peña
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)

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.

Keywords

Accurate Computation Gaussian Elimination Nonnegative Matrice Total Positivity Positive Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dpto. de Matemática AplicadaUniversidad de ZaragozaZaragozaSpain

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