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Symbiosis between Linear Algebra and Optimization
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
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
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
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
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 ...