Abstract As is well known, a rank- r matrix can be recovered from a cross of r linearly independent columns and rows, and an arbitrary matrix can be interpolated on the cross entries. Other entries… Expand

Abstract Let an m × n matrix A be approximated by a rank- r matrix with an accuracy e. We prove that it is possible to choose r columns and r rows of A forming a so-called pseudoskeleton component… Expand

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… Expand

Lecture 1: metric space some useful definitions nested balls normed space popular vector norms matrix norms equivalent norms operator norms. Lecture 2: scalar product length of a vector isometric… Expand

We consider the eigenvalue and singular-value distributions for m-level Toeplitz matrices generated by a complex-valued periodic function ƒ of m real variables. We show that familiar formulations for… Expand

We propose some asymptotically tighter bound in terms of the ratio of the smallest eigenvalue of the hermitian part and the norm of some nonsymmetric matrix, based on a GMRES error estimate.Expand

The mosaic-skeleton method was bred in a simple observation that rather large blocks in very large matrices coming from integral formulations can be approximated accurately by a sum of just few rank-one matrices (skeletons).Expand