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Now showing items 31-40 of 69

#### Note on a Generalized Sylvester Equation

(1998-10-15)

In this note we show how to compute the minimum-norm, least
squares solution of the generalized Sylvester equation
\[
AX + YB = C,
\]
(Also cross-referenced as UMIACS-TR-92-59)

#### On the Adjoint Matrix

(1998-10-15)

The adjoint $A\adj$ of a matrix $A$ is the transpose of the matrix of the
cofactors of the elements of $A$. The computation of the adjoint from
its definition involves the computation of $n^{2}$ determinants of
order ...

#### An Analysis of the Rayleigh--Ritz Method for Approximating Eigenspaces\symbolmark{1}

(1999-05-11)

This paper concerns the Rayleigh--Ritz method for computing an
approximation to an eigenspace $\clx$ of a general matrix $A$ from a
subspace $\clw$ that contains an approximation to $\clx$. The method
produces a pair $(N, ...

#### 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 ...

#### Time-Domain Extraction of Broad-Band Sources by Tikhonov-Phillips Regularization of Triangular Toeplitz Kernels*

(1998-10-15)

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 ...

#### 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 Method of Pure Truncation for Approximating Stationary Probabilities

(2003-08-01)

This paper is concerned with approximating the leading components of
the stationary vector of a semi-infinite discrete markov chain. The
most widely treated method extracts a leading principal submatrix from
the matrix ...

#### On the Perturbation of Schur Complements in Positive Semidefinite Matrices

(1998-10-15)

This note gives perturbation bounds for the Schur
complement of a positive definite matrix in a positive semidefinite matrix.
(Also cross-referenced as UMIACS-TR-95-38)

#### On the Powers of a Matrix with Perturbations

(2002-01-31)

Let $A$ be a matrix of order $n$. The properties of the powers
$A^{k}$ of $A$ have been extensively studied in the literature.
This paper concerns the perturbed powers
\[
P_{k} = (A+E_{k})(A+E_{k-1})\cdots(A+E_{1}), ...

#### On Sublinear Convergence

(1998-10-15)

This note develops a theory of sublinearly converging
sequences, including a categorization of the rates of convergence and a
method for determining the rate from an iteration function.
(Also cross-referenced as UMIACS-TR-95-92)