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Now showing items 1-10 of 64

#### On the Early History of the Singular Value Decomposition

(1998-10-15)

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 ...

#### Direction-of-Arrival Estimation Using the Rank-Revealing URV Decomposition

(1998-10-15)

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 ...

#### Communication and Matrix Computations on Large Message Passing Systems

(1998-10-15)

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 ...

#### On the Stability of Sequential Updates and Downdates

(1998-10-15)

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 ...

#### On the Perturbation of LU and Cholesky Factors*

(1998-10-15)

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 ...

#### Determining Rank in the Presence of Error

(1998-10-15)

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 ...

#### Scaling for Orthogonality

(1998-10-15)

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 ...

#### Incremental Condition Calculation and Column Selection

(1998-10-15)

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 ...

#### QR Sometimes Beats Jacobi

(1998-10-15)

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)

#### SRRIT--A FORTRAN Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix

(1998-10-15)

{\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 ...