Rectangular maximum volume and projective volume search algorithms
For researchers in matrix approximation and numerical linear algebra, providing improved methods for submatrix selection with theoretical guarantees.
The paper proposes new algorithms for finding submatrices with maximal volume and large projective volume, demonstrating their effectiveness in cross approximations and proving estimates for strongly nondegenerate submatrix search.
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.