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Each iteration of the multishift QR algorithm of Bai and Demmel requires the computation of a \shift vector" deened by m shifts of the origin of the spectrum that control the convergence of the process. A common choice of shifts consists of the eigenvalues of the trailing principal submatrix of order m, and current practice includes the computation of these… (More)

Moler and Morrison have described an iterative algorithm for the computation of the Pythagorean sum (a' + b2)"' of two real numbers a and b. This algorithm is immune to unwarrantedfloating-point overjows, has a cubic rate of convergence, and is easily transportable. This paper, which shows that the algorithm is essentially Harley's method applied to the… (More)

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