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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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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

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 ...

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 ...

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 ...