An accelerated alternating minimization algorithm is developed for low-rank matrix approximation in the Chebyshev norm, along with a proof that its limit points satisfy a new necessary optimality condition called 2-way alternance of rank r.
Rectangular maximum volume and projective volume search algorithms
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abstract
New methods for finding submatrices of (locally) maximal volume and large projective volume are proposed and studied. Detailed analysis is also carried out for existing methods. The effectiveness of the new methods is shown in the construction of cross approximations, and estimates are also proved in the case of their application for the search for a strongly nondegenerate submatrix. Much attention is also paid to the choice of the starting submatrix.
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UNVERDICTED 2representative citing papers
A column-exchange modification to greedy volume-maximization subset selection achieves the same bounds on the pseudoinverse representation error as existing methods but with faster runtime for n much larger than m, plus a new upper bound on the number of exchanges needed.
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Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm
An accelerated alternating minimization algorithm is developed for low-rank matrix approximation in the Chebyshev norm, along with a proof that its limit points satisfy a new necessary optimality condition called 2-way alternance of rank r.
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Subset selection for matrices by column exchange
A column-exchange modification to greedy volume-maximization subset selection achieves the same bounds on the pseudoinverse representation error as existing methods but with faster runtime for n much larger than m, plus a new upper bound on the number of exchanges needed.