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Journals and Conferences
Abstract. Block implementations of the conjugate-gradients method for the solution of a linear system must deal with linear dependences that may appear in the descent or residual blocks in the course of the iteration. New algorithms presented here avoid rank estimation and deflation through the use of changes of bases and algorithmic reformulations that… (More)
Each iteration of the multishift QR algorithm of Bai and Demmel requires the computation of a “shift vector” defined bym 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 orderm, 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)
A new analysis of the two types of Householder reflections shows that the second type stably defined by Parlett has a better ability to propagate information borne by its driving vector. The results are extended to the Davis–Kahan rotation.
This paper presents an extension of the domain of the APL Domino function to systems of linear equations the matrix of which contains linearly dependent columns. This extension is based on the concepts of minimum and basic least squares solutions, and pseudo-inverses [1,2], which have found many applications in various areas such as statistics  and… (More)
A transposition matrix may reveal information on the spectrum of the matrix to which it applies. © 2009 Elsevier B.V. All rights reserved.
Floating-point arithmetic is the design almost universally accepted for computers dealing with so-called scientific computations. It was present in some of the earliest machines and successfully survived the controversies that followed its first implementations. Since then, it has been consistently available in the hardware of many systems and it has… (More)