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Now showing items 1-10 of 69

#### Numerical Methods for M/G/1 Type Queues

(1998-10-15)

Queues of M/G/1 type give rise to infinite embedded
Markov chains whose transition matrices are upper block Hessenberg. The
traditional algorithms for solving these queues have involved the
computation of an intermediate ...

#### A Residual Inverse Power Method

(2007-02)

The inverse power method involves solving shifted equations of the
form $(A -\sigma I)v = u$. This paper describes a variant method in
which shifted equations may be solved to a fixed reduced accuracy
without affecting ...

#### Gaussian Elimination, Perturbation Theory and Markov Chains

(1998-10-15)

The purpose of this paper is to describe the special problems that
emerge when Gaussian elimination is used to determinin the
steady-state vector of a Markov chain.
(Also cross-referenced as UMIACS-TR-92-23)

#### On the Sensitivity of Nearly Uncoupled Markov Chains

(1998-10-15)

Nearly uncoupled Markov chains (aka nearly completely decomposable Markov
chains) arise in a variety of applications, where they model loosely
coupled systems. In such systems it may be difficult to determine the
transitions ...

#### 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 ...

#### Adjusting the Rayleigh Quotient in Semiorthogonal Lanczos Methods

(2001-05-10)

In a semiorthogonal Lanczos algorithm, the orthogonality of the
Lanczos vectors is allowed to deteriorate to roughly the square root
of the rounding unit, after which the current vectors are
reorthogonalized. A theorem ...

#### 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 ...

#### EIGENTEST: A Test Matrix Generator for Large-Scale Eigenproblems

(2006-02-13)

Eigentest is a package that produces real test matrices with known
eigensystems. A test matrix, called an eigenmat, is generated in a
factored form, in which the user can specify the eigenvalues and has
some control ...

#### Perturbation Theory for the Singular Value Decomposition

(1998-10-15)

The singular value decomposition has a number of applications in digital
signal processing. However, the the decomposition must be computed from a
matrix consisting of both signal and noise. It is therefore important ...