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Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
Inverse iteration is one of the most widely used algorithms in practical linear algebra but an understanding of its main numerical properties has developed piecemeal over the last thirty years: aExpand
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The Least Squares Problem and Pseudo-Inverses
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On the stability of Gauss-Jordan elimination with pivoting
The stability of the Gauss-Jordan algorithm with partial pivoting for the solution of general systems of linear equations is commonly regarded as suspect, and in many respects suspicions are unfounded. Expand
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TheQ R algorithm for real hessenberg matrices
The QR algorithm of Francis [1] and Kublanovskaya [4] with shifts of origin is described by the relations $$ \matrix{ {{Q_s}({A_s} - {k_s}I) = {R_s},} & {{A_{s + 1}} = {R_s}Q_s^T + {k_s}I,} &Expand
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The Calculation of Specified Eigenvectors by Inverse Iteration
When an approximation µ is known to an eigenvalue of a matrix A, inverse iteration provides an efficient algorithm for computing the corresponding eigenvector. It consists essentially of theExpand
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Iterative Refinement of the Solution of a Positive Definite System of Equations
In an earlier paper in this series [1] the solution of a system of equations Ax=b with a positive definite matrix of coefficients was described; this was based on the Cholesky factorization of A. IfExpand
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