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Now showing items 21-30 of 69

#### Addendum to ``A Krylov--Schur Algorithm for Large Eigenproblems"

(2002-01-31)

In this addendum to an earlier paper by the author, it is shown how to
compute a Krylov decomposition corresponding to an arbitrary
Rayleigh-Quotient. This decomposition can be used to restart an
Arnoldi process, with ...

#### Updating URV Decompositions in Parallel

(1998-10-15)

A URV decomposition of a matrix is a factorization of the matrix into
the product of a unitary matrix (U), an upper triangular matrix (R),
and another unitary matrix (V). In an earlier paper [UMIACS-TR-90-86]
it was shown ...

#### Error Analysis of the Quasi-Gram--Schmidt Algorithm

(2004-04-19)

Let the $n{\times}p$ $(n\geq p)$ matrix $X$ have the QR~factorization
$X = QR$, where $R$ is an upper triangular matrix of order $p$ and $Q$
is orthonormal. This widely used decomposition has the drawback that
$Q$ is ...

#### On the Perturbation of LU, Cholesky, and QR Factorizations

(1998-10-15)

To appear in SIMAX
In this paper error bounds are derived for a first order expansion of
the LU factorization of a perturbation of the identity. The results
are applied to obtain perturbation expansions of the LU, Cholesky, ...

#### Two Algorithms for the The Efficient Computation of Truncated Pivoted QR Approximations to a Sparse Matrix

(1998-10-15)

In this note we propose two algorithms to compute truncated pivoted QR
approximations to a sparse matrix. One is based on the Gram--Schmidt
algorithm, and the other on Householder triangularization. Both
algorithms leave ...

#### On a New Way of Solving the Linear Equations that Arise in the Method of Least Squares

(1998-10-15)

Translated by G. W. Stewart
This report contains a translation of a paper of C. G. J. Jacobi,
``Ueber eine neue Aufl\"osungsart der bei der Methode der kleinsten
Quadrate vorkommenden line\"aren Gleichungen,'' which ...

#### 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 Solution of Block Hessenberg Systems

(1998-10-15)

This paper describes a divide-and-conquer strategy for solving block
Hessenberg systems. For dense matrices the method is a little more
efficient than Gaussian elimination; however, because it works almost
entirely with ...

#### Stochastic Perturbation Theory

(1998-10-15)

Appeared in SIAM Review 32 (1990) 576--610.
In this paper classical matrix perturbation theory is approached from
a probabilistic point of view. The perturbed quantity is
approximated by a first order perturbation ...

#### On Markov Chains with Sluggish Transients

(1998-10-15)

In this note it is shown how to construct a Markov chain whose
subdominant eigenvalue does not predict the decay of its transient.
(Also cross-referenced as UMIACS-TR-94-77)