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We examine preconditioners for the discrete indefinite Helmholtz equation on a three-dimensional box-shaped domain with Sommerfeld-like boundary conditions. The preconditioners are of two types. The first is derived by ...

In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that ...

A sentence extract summary of a document is a subset of the document's sentences that contains the main ideas in the document. We present two approaches to generating such summaries. The first uses a pivoted QR ...

We derive algorithms for computing a semidiscrete approximation to a matrix in the Frobenius and weighted norms. The approximation is formed as a weighted sum of outer products of vectors whose elements are plus or minus ...

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 ...

Standard multigrid algorithms have proven ineffective for the solution of discretizations of Helmholtz equations. In this work we modify the standard algorithm by adding GMRES iterations at coarse levels and as an outer ...

The vast amount of textual information available today is useless unless it can be effectively and efficiently searched. In information retrieval, we wish to match queries with relevant documents. Documents can be ...

With the electronic storage of documents comes the possibility of building search engines that can automatically choose documents relevant to a given set of topics. In information retrieval, we wish to match queries ...

Algorithms for computing images result in an estimate of an image. The image may result from deblurring a measured image, from deconvolving a set of measurements, or from computing an image by modeling physical processes ...

We study problems for which the iterative method \gmr for solving linear systems of equations makes no progress in its initial iterations. Our tool for analysis is a nonlinear system of equations, the stagnation ...