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This paper surveys the contributions of five mathematicians\,---\,Eugenio Beltrami (1835--1899), Camille Jordan (1838--1921), James Joseph Sylvester (1814--1897), Erhard Schmidt (1876--1959), and Hermann Weyl (1885--1955 ...

Appeared in Proceedings of ACASSP-91. An algorithm for updating the null space of a matrix is described. The algorithm is based on a new decomposition, called the URV decomposition, which can be updated in $O(N^2)$ and ...

This paper is concerned with the consequences for matrix computations of having a rather large number of general purpose processors, say ten or twenty thousand, connected in a network in such a way that a processor can ...

The updating and downdating of QR decompositions has important applications in a number of areas. There is essentially one standard updating algorithm, based on plane rotations, which is backwards stable. Three downdating ...

In a recent paper, Chang and Paige have shown that the usual perturbation bounds for Cholesky factors can systematically overestimate the errors. In this note we sharpen their results and extend them to the factors of ...

The problem of determining rank in the presence of error occurs in a number of applications. The usual approach is to compute a rank-revealing decomposition and make a decision about the rank by examining the small elements ...

In updating algorthms where orthogonal transformations are accumulated, it is important to preserve the orthogonality of the product in the presence of rounding error. Moonen, Van Dooren, and Vandewalle have pointed out ...

This paper describes a method for calculating the condition number of a matrix in the Frobenius norm that can be used to select columns in the course of computing a QR decomposition. When the number of rows of the matrix ...

This note exhibits a symmetric matrix having a small eigenvalue that is computed accurately by the QR algorithm but not by Jacobi's method. (Also cross-referenced as UMIACS-TR-95-32)

{\sl SRRIT} is a FORTRAN program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix $A$ by the method of simultaneous iteration \cite{stewart76a}. Specifically, given an integer ...