Accurate computation of the smallest eigenvalue of a diagonally dominant M -matrix

作者: Attahiru Sule Alfa , Jungong Xue , Qiang Ye

DOI: 10.1090/S0025-5718-01-01325-4

关键词: Machine epsilonInverseM-matrixEigenvalues and eigenvectorsDiagonally dominant matrixCombinatoricsComputationApplied mathematicsMathematicsRound-off error

摘要: If each off-diagonal entry and the sum of row a diagonally dominant M-matrix are known to certain relative accuracy, then its smallest eigenvalue entries inverse same order accuracy independent any condition numbers. In this paper, we devise algorithms that compute these quantities with errors in magnitude machine precision. Rounding error analysis numerical examples presented demonstrate behaviour algorithms.

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