We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This is then used to provide cellular structure generalized Schur algebras associated an arbitrary algebra. Applications the cellularity wreath product A ? S d are also considered.

A hybrid linear solver based on the Schur complement method has great potential to be a general purpose solver scalable on tens of thousands of processors. It is imperative to exploit two levels of parallelism; namely, solving independent subdomains in parallel and using multiple processors per subdomain. This hierarchical parallelism can lead to a scalable implementation which maintains numeri...

The current algorithms use either the full form or Schur decomposition of matrix in inverse scaling and squaring method to compute logarithm. consists two main calculations: taking a square root evaluating Padé approximants. In this work, we suggest using structure preserving iteration as an alternative Denman-Beavers for root. Numerical experiments show that while preserves Hamiltonian logarit...

We study two different decomposition algorithms for the general (nonconvex) partially separable nonlinear program (PSP): bilevel decomposition algorithms (BDAs) and Schur interior-point methods (SIPMs). BDAs solve the problem by breaking it into a master problem and a set of independent subproblems, forming a type of bilevel program. SIPMs, on the other hand, apply an interior-point technique t...

The quadratic matrix equation AX2 + B X +C = 0 in n ×n matrices arises in applications and is of intrinsic interest as one of the simplest nonlinear matrix equations. We give a complete characterization of solutions in terms of the generalized Schur decomposition and describe and compare various numerical solution techniques. In particular, we give a thorough treatment of functional iteration m...

We show that for general linear groups GLn(q) as well as for q-Schur algebras the knowledge of the modular Alvis-Curtis duality over fields of characteristic l, l ∤ q, is equivalent to the knowledge of the decomposition numbers.

We present a domain decomposition method suitable for the drift-diiusion equations. The new scheme is applied to the linear systems resulting from Gummel's method and corresponds to a preconditioned conjugate gradient technique for the Schur complement of the linear systems. In designing the preconditioner two problems are addressed : anisotropic phenomena and large scale variations in the magn...

We present and prove Rogers–Schur–Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model M(p, p). The proof uses the continued fraction decomposition of p/p introduced by Takahashi and Suzuki for the study of the Bethe’s Ansatz equations of the XXZ model and gives a general method to construct polynomial generalizations of the fermionic form of the characters wh...