Entrywise relative perturbation theory for nonsingularM-matrices and applications
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This paper establishes a new entrywise relative perturbation result for the inverse of a nonsingularM-matrixA. It is shown that a version of Gaussian elimination with one step of iterative refinement solves the systemAx =b, whereb is nonnegative, with small entrywise relative error. IfA is tridiagonal, the Gaussian elimination alone suffices.
Key wordsM-matrix Gaussian elimination regular splitting iterative refinement error analysis
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