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Now showing items 21-30 of 64

#### Rounding Errors in Solving Block Hessenberg Systems

(1998-10-15)

A rounding error analysis is presented for a divide-and-conquer
algorithm to solve linear systems with block Hessenberg matrices.
Conditions are derived under which the algorithm computes a
backward stable solution. ...

#### 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 ...

#### 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 ...

#### Backward Error Bounds for Approximate Krylov Subspaces

(2001-05-10)

Let $A$ be a matrix of order $n$ and let $\clu\subset\comp^{n}$ be a
subspace of dimension $k$. In this note we determine a matrix $E$ of
minimal norm such that $\clu$ is a Krylov subspace of $A+E$.
(Cross-referenced ...

#### 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)

#### 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 ...

#### On Infinitely Many Algorithms for Solving Equations

(1998-10-15)

Translated by G. W. Stewart
This report contains a translation of ``Ueber unendlich viele
Algorithmen zur Aufl\"osung der Gleichungen,'' a paper by E.
Schr\"oder which appeared in {\it Mathematische Annalen\/} in 1870.
(Also ...

#### On a Direct Method for the Solution of Nearly Uncoupled Markov Chains

(1998-10-15)

This note is concerned with the accuracy of the solution of nearly
uncoupled Markov chains by a direct method based on the LU
decomposition. It is shown that plain Gaussian elimination may fail
in the presence of rounding ...

#### Lanczos and Linear Systems

(1998-10-15)

Lanczos's major contributions to the numerical solution of linear
equations are contained in two papers: ``An Iteration Method for the
Solution of the Eigenvalue Problem of Linear Differential and
Integral Operators'' and ...

#### Error Analysis of QR Updating with Exponential Windowing

(1998-10-15)

To appear in Mathematics of Computation
Exponential windowing is a widely used technique for suppressing the
effects of old data as new data is added to a matrix. Specifically,
given an $n\times p$ matrix $X_n$ and a ...