# Search

Now showing items 21-29 of 29

#### Adaptive Use of Iterative Methods in Interior Point Methods for Linear Programming

(1998-10-15)

In this work we devise efficient algorithms for finding the search
directions for interior point methods applied to linear programming
problems. There are two innovations. The first is the use of updating of
preconditioners ...

#### Fast Iterative Image Restoration with a Spatially-Varying PSF

(1998-10-15)

We describe how to efficiently apply a spatially-variant
blurring operator using linear interpolation of measured point spread functions.
Numerical experiments illustrate that substantially better resolution
can be obtained ...

#### A polynomial-time interior-point method for conic optimization, with inexact barrier evaluations

(2008-04)

We consider a primal-dual short-step interior-point method for conic convex optimization problems for which exact evaluation of the gradient and Hessian of the primal and dual barrier functions is either impossible or ...

#### Exploiting Structure of Symmetric or Triangular Matrices on a GPU

(2008-01)

Matrix computations are expensive, and GPUs have the potential to
deliver results at reduced cost by exploiting parallel computation.
We focus on dense matrices of the form A D2 A^T, where
A is an m x n matrix (m less ...

#### BFGS with Update Skipping and Varying Memory

(1998-10-15)

We give conditions under which limited-memory quasi-Newton methods
with exact line searches will terminate in $n$ steps when minimizing
$n$-dimensional quadratic functions. We show that although all
Broyden family methods ...

#### Pivoted Cauchy-like Preconditioners for Regularized Solution of Ill-Posed Problems

(1998-10-15)

Many ill-posed problems are solved using a discretization that
results in a least squares problem or a linear system involving a
Toeplitz matrix. The exact solution to such problems
is often hopelessly contaminated by ...

#### Overcomimg Instability in Computing the Fundamental Matrix for a Markov Chain

(1998-10-15)

We present an algorithm for solving linear systems involving
the probability or rate matrix for a Markov chain.
It is based on a UL factorization but works only with a
submatrix of the factor U. We demonstrate its utility
on ...

#### Why Broyden's Nonsymmetric Method Terminates on linear equations

(1998-10-15)

Abstract. The family of algorithms introduced by Broyden in 1965 for
solving systems of nonlinear equations has been used quite effectively on
a variety of problems. In 1979, Gay proved the then surprising result
that ...

#### Conjugate Gradients and Related KMP Algorithms: The Beginnings

(1998-10-15)

In the late 1940's and early 1950's, newly available computing
machines generated intense interest in solving ``large'' systems
of linear equations. Among the algorithms developed were several
related methods, all of ...