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Mathematics of Computation

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A stable test to check if a matrix is a nonsingular $M$-matrix

Author: J. M. Peña
Translated by:
Journal: Math. Comp. 73 (2004), 1385-1392
MSC (2000): Primary 65F30, 65F05, 65G99
Published electronically: February 18, 2004
MathSciNet review: 2047092
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Abstract: A stable test for checking if a matrix is a nonsingular $M$-matrix is presented. Its computational cost is, in the worst case, $O(n^{2})$elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius less than 1.

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Additional Information

J. M. Peña
Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, 50006 Zaragoza, Spain

Keywords: Test for $M$-matrices, diagonal dominance, stability, growth factor
Received by editor(s): January 11, 2002
Received by editor(s) in revised form: January 4, 2003
Published electronically: February 18, 2004
Additional Notes: This research has been partially supported by the Spanish Research Grant CICYT BFM2000-1253.
Article copyright: © Copyright 2004 American Mathematical Society