Article history: Received 19 July 2009 Accepted 27 July 2009 Available online 21 August 2009 Submitted by V. Sergeichuk AMS classification: 15A12 65F10 65F15

For d-dimensional tensors with possibly large d > 3, an hierarchical data structure, called the Tree-Tucker format, is presented as an alternative to the canonical decomposition. It hasâ€¦ (More)

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 fewâ€¦ (More)

Starting from an GMRES error estimate proposed by Elman in terms of the ratio of the smallest eigenvalue of the hermitian part and the norm of some non-symmetric matrix, we propose someâ€¦ (More)

Abstract. We consider Tucker-like approximations with an r Ã— r Ã— r core tensor for threedimensional nÃ—nÃ—n arrays in the case of r Â¿ n and possibly very large n (up to 104âˆ’106). As the approximationâ€¦ (More)

The eigenvalue clustering of matrices Sâˆ’1 n An and C âˆ’1 n An is experimentally studied, where An, Sn and Cn respectively are Toeplitz matrices, Strang, and optimal circulant preconditioners generatedâ€¦ (More)

A purely algebraic approach to solving very large general unstructured dense linear systems, in particular, those that arise in 3D boundary integral applications is suggested. We call this techniqueâ€¦ (More)

Usually when singular values are clustered the eigenvalues behave similarly However it is not the case if we make no assumptions Here we present examples when the singular values are clusteredâ€¦ (More)