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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 ...
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 ...
Computation and Uses of the Semidiscrete Matrix Decomposition
(1999-04-06)
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 ...
Adaptive Use of Iterative Methods in Predictor-Corrector Interior Point Methods for Linear Programming
(1999-04-06)
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 ...
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
(1999-08-27)
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 ...