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Optimization by direct search in matrix computations. (English) Zbl 0776.65047

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 J. E. Dennis jun. and V. J. Torczon [SIAM J. Optimization 1, No. 4, 448-474 (1991; Zbl 0754.90051)].

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
65F05 Direct numerical methods for linear systems and matrix inversion
65F35 Numerical computation of matrix norms, conditioning, scaling

Citations:

Zbl 0754.90051

Software:

LAPACK; subplex
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