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Now showing items 11-20 of 69

#### Perturbation Theory for Rectangular Matrix Pencils

(1998-10-15)

The theory of eigenvalues and eigenvectors of rectangular matrix
pencils is complicated by the fact that arbitrarily small
perturbations of the pencil can cause them disappear. However, there
are applications in which the ...

#### Direction of Arrival and the Rank-Revealing URV Decomposition

(1998-10-15)

In many practical direction-of-arrival (DOA) problems the number
of sources and their directions from an antenna array do not remain
stationary. Hence a practical DOA algorithm must be able to track
changes with a minimal ...

#### Two Simple Residual Bounds for the Eigenvalues of Hermitian Matrices

(1998-10-15)

Let $A$ be Hermitian and let the orthonormal columns of $X$ span an
approximate invariant subspace of $X$. Then the residual $R = AX-XM$
$(M=X\ctp AX)$ will be small. The theorems of this paper bound the
distance of the ...

#### 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 ...

#### An Iterative Method for Solving Linear Inequalities

(1995-02-06)

This paper describes and analyzes a method for finding nontrivial
solutions of the inequality $Ax \geq 0$, where $A$ is an $m \times n$
matrix of rank $n$. The method is based on the observation that a
certain function ...

#### 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 ...

#### 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 ...

#### 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 ...