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Now showing items 1-10 of 17

#### 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 ...

#### 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 ...

#### 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 ...

#### Analysis of the Residual Arnoldi Method

(2007-10-15)

The Arnoldi method generates a nested squences of orthonormal bases
$U_{1},U_{2}, \ldots$ by orthonormalizing $Au_{k}$ against $U_{k}$.
Frequently these bases contain increasingly accurate approximations of
eigenparis ...

#### The Gram-Schmidt Algorithm and Its Variations

(2006-01-13)

The Gram--Schmidt algorithm is a widely used method for
orthogonalizing a sequence of vectors. It comes in two forms:
classical Gram--Schmidt and modified Gram--Schmidt, each of whose
operations can be ordered in ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...