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Pseudoskeleton approximation and some other problems require the knowledge of sufficiently well-conditioned submatrix in a large-scale matrix. The quality of a submatrix can be measured by modulus of its determinant, also known as volume. In this paper we discuss a search algorithm for the maximum-volume submatrix which already proved to be useful in several matrix and tensor approximation algorithms. We investigate the behavior of this algorithm on random matrices and present some its applications, including maximization of a bivariate functional.

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