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Now showing items 11-20 of 64

#### On the Perturbation of Markov Chains with Nearly Transient States

(1998-10-15)

To Appear in Numerische Mathematik
Let $A$ be an irreducible stochastic matrix of the form
\[
A = \bmx{cc} A_{11} & E_{12} \\ A_{21} & A_{22} \emx.
\]
If $E_{22}$ were zero, the states corresponding to $A_{22}$ would ...

#### 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 ...

#### On Orthogonalization in the Inverse Power Method

(1999-10-13)

When the inverse power method is used to compute eigenvectors of a
symmetric matrix corresponding to close eigenvalues, the computed
eigenvectors may not be orthogonal. The cure for the problem is to
orthogonalize the ...

#### Three Results on Iterative Regularization

(1998-11-03)

In this paper we present three theorems which give insight into the
regularizing properties of {\minres}. While our theory does not
completely characterize the regularizing behavior of the algorithm, it
provides a partial ...

#### On the Convergence of Ritz Values, Ritz Vectors, and Refined Ritz Vectors\symbolmark

(1999-01-29)

This paper concerns the Rayleigh--Ritz method for computing an
approximation to an eigenpair $(\lambda, x)$ of a non-Hermitian matrix
$A$. Given a subspace $\clw$ that contains an approximation to $x$,
this method returns ...

#### 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 ...

#### Gauss, Statistics, and Gaussian Elimination

(1998-10-15)

This report gives a historical survey of Gauss's work on the solution
of linear systems.
(Also cross-referenced as UMIACS-TR-94-78)

#### The Triangular Matrices of Gaussian Elimination and Related Decompositions

(1998-10-15)

It has become a commonplace that triangular systems are solved to
higher accuracy than their condition would warrant. This observation is
not true in general, and counterexamples are easy to construct. However,
it is often ...

#### On Graded QR Decompositions of Products of Matrices

(1998-10-15)

This paper is concerned with the singular values and vectors of a
product $M_{m}=A_{1}A_{2}\cdots A_{m}$ of matrices of order $n$. The
chief difficulty with computing them from directly from $M_{m}$ is
that with increasing ...

#### Time-Domain Extraction of Broad-Band Sources by Tikhonov-Phillips Regularization of Triangular Toeplitz Kernels*

(1998-10-15)

Single receiver source deconvolution in a shallow water
environment is an ill-posed problem whose difficulty is compounded by the
multipath nature of the propagation operator. If only sources that are
quiescent prior to ...