Optimization by Direct Search in Matrix Computations
Copyright policy )Optimization by Direct Search in Matrix Computations
Many questions about algorithms in matrix computations can be expressed in terms of the maximum value of some easily computable function \(f\). For many algorithms it is known that direct search is capable of revealing instability or proof performance. In this work the following topics in matrix computations are studied by using direct search methods: condition estimators, matrix inversion, Vandermonde system solvers, matrix multiplication, QR-factorization. The author experiments with two methods: the alternating direction method and the multidirectional search method of \textit{J. E. Dennis jun.} and \textit{V. J. Torczon} [SIAM J. Optimization 1, No. 4, 448-474 (1991; Zbl 0754.90051)].
- University of Manchester United Kingdom
- University of Manchester United Kingdom
Numerical computation of matrix norms, conditioning, scaling, matrix multiplication, condition estimators, Direct numerical methods for linear systems and matrix inversion, matrix inversion, alternating direction method, Vandermonde system solvers, Numerical mathematical programming methods, Nonlinear programming, QR- factorization, Gaussian elimination, multidirectional search method, matrix condition number estimation, direct search methods, matrix computations
Numerical computation of matrix norms, conditioning, scaling, matrix multiplication, condition estimators, Direct numerical methods for linear systems and matrix inversion, matrix inversion, alternating direction method, Vandermonde system solvers, Numerical mathematical programming methods, Nonlinear programming, QR- factorization, Gaussian elimination, multidirectional search method, matrix condition number estimation, direct search methods, matrix computations
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