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Building an Old-Fashioned Sparse Solver
(2003-09-25)
A sparse matrix is a matrix with very few nonzero elements. Many
applications in diverse fields give rise to linear systems of the form
$Ax = b$, where $A$ is sparse. The problem in solving these systems
is to take ...
An Elsner-Like Perturbation Theorem for Generalized Eigenvalues
(2003-12-18)
In 1985 Elsner established a general bound on the distance between an
eigenvalue of a matrix and the closest eigenvalue of a perturbation of
that matrix. In this note, we show that a similar result holds for
the ...
Memory Leaks in Derived Types Revisited
(2003-09-02)
In a note in the {\it Fortran Forum\/}, Markus describes a technique
for avoiding memory leaks with derived types. In this note, we show
by a simple example that this technique does not work when the object
in question ...
A Fortran 95 Matrix Wrapper
(2003-09-02)
{\Matran} is an wrapper written in Fortran~95 that implements matrix
operations and computes matrix decompositions using {\lapack} and the
{\blas}. This document describes a preliminary release of {\matran},
which ...
On the Method of Pure Truncation for Approximating Stationary Probabilities
(2003-08-01)
This paper is concerned with approximating the leading components of
the stationary vector of a semi-infinite discrete markov chain. The
most widely treated method extracts a leading principal submatrix from
the matrix ...