Let B be a block of an Iwahori–Hecke algebra or q-Schur algebra of the symmetric group. The decomposition matrix for B may be obtained from the decomposition matrix of the corresponding block B′ in infinite characteristic by post-multiplying by an adjustment matrix; since (by a deep theorem of Ariki) there is an algorithm for computing the decomposition matrix for B′, the hard part of the decom...

We have designed, implemented and tested (by simulation on a serial computer) the new dynamic ordering for the parallel one-sided block-Jacobi SVD algorithm. Our idea is based on the estimation of the cosines of principal angles between two block columns X and Y of the same width without explicitly forming the matrix product XY (or Y X) and computing its SVD. Instead, we propose to use a fixed ...

A new facile fabrication approach to generate polymeric nanostructures is described. Block copolymers containing immiscible segments can self-assemble to generate ordered nanostructures, such as cylinders of one block in a matrix of the other in the bulk, which can then be sectioned on the nanoscale using a microtome (nanoskiving). Dispersing these sections in a selective solvent for the matrix...

We investigate the properties of block matrices with block banded inverses to derive efficient matrix inversion algorithms for such matrices. In particular, we derive the following: (1) a recursive algorithm to invert a full matrix whose inverse is structured as a block tridiagonal matrix; (2) a recursive algorithm to compute the inverse of a structured block tridiagonal matrix. These algorithm...

This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the “block-sparse” case. In this regard, it first specifies conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for average-case analys...