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Now showing items 1-10 of 29

#### Modified Cholesky Algorithms: A Catalog with New Approaches

(2006-08-08)

Given an $n \times n$ symmetric possibly indefinite matrix $A$,
a modified Cholesky algorithm computes a factorization of
the positive definite
matrix $A+E$, where $E$ is a correction matrix.
Since the factorization ...

#### Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems

(1998-10-15)

Numerical solution of ill-posed problems is often accomplished by
discretization (projection onto a finite dimensional subspace) followed by
regularization. If the discrete problem has high dimension, though,
typically ...

#### TIKHONOV REGULARIZATION AND TOTAL LEAST SQUARES

(1998-10-15)

Discretizations of inverse problems lead to systems of linear equations
with a highly ill-conditioned coefficient matrix, and in order to
compute stable solutions to these systems it is necessary to apply
regularization ...

#### Symbiosis between Linear Algebra and Optimization

(1999-05-28)

The efficiency and effectiveness of most optimization algorithms
hinges on the numerical linear algebra algorithms that they utilize.
Effective linear algebra is crucial to their success, and because
of this, optimization ...

#### A Parallel Inexact Newton Method Using a Krylov Multisplitting Algorithm

(1998-10-15)

Abstract. We present a paraUel variant of the inexact Newton algorithm
that uses the Krylov multisplitting algorithm (KMS) to compute the
approxrmate Newton direction. The algorithm can be used for solving
unconstrained ...

#### Restoring Images Degraded by Spatially-Variant Blur

(1998-10-15)

Restoration of images that have been blurred by the effects
of a Gaussian blurring function is an ill-posed but well-studied
problem. Any blur that is spatially invariant can be expressed
as a convolution kernel in an ...

#### Regularization Algorithms Based on Total Least Squares

(1998-10-15)

Discretizations of inverse problems lead to systems of linear equations
with a highly ill-conditioned coefficient matrix, and in order to
compute stable solutions to these systems it is necessary to apply
regularization ...

#### Image Restoration through Subimages and Confidence Images

(2000-07-20)

Some very effective but expensive image reconstruction algorithms cannot
be applied to large images because of their cost. In this work, we first
show how to apply such algorithms to subimages, giving improved
reconstruction ...

#### Near-Optimal Parameters for Tikhonov and Other Regularization Methods

(1999-04-06)

Choosing the regularization parameter for an ill-posed problem is an art
based on good heuristics and prior knowledge of the noise in the
observations. In this work we propose choosing the parameter, without a
priori ...

#### Efficient Iterative Algorithms for the Stochastic Finite Element Method with Application to Acoustic Scattering

(2002-12-19)

In this study, we describe the algebraic computations required
to
implement the stochastic finite element method for solving problems in
which uncertainty is restricted to right hand side data coming from
forcing ...