A methodology for preconditioning discrete stress analysis systems using robust scalar algebraic multigrid (AMG) solvers is evaluated in the context of problems that arise in microfabrication technology. The principle idea is to apply an AMG solver in a segregated way to the series of scalar block matrix problems corresponding to different displacement vector components, thus yielding a block d...

A block negacyclic Bush-type Hadamard matrix of order 36 is used in a symmetric BGW(26, 25, 24) with zero diagonal over a cyclic group of order 12 to construct a twin strongly regular graph with parameters v=936, k=375, l=m=150 whose points can be partitioned in 26 cocliques of size 36. The same Hadamard matrix then is used in a symmetric BGW(50, 49, 48) with zero diagonal over a cyclic group o...

We consider preconditioned Krylov subspace methods for solving large sparse linear systems under the assumption that the coefficient matrix is a (possibly singular) M -matrix. The matrices are partitioned into 2×2 block form using graph partitioning. Approximations to the Schur complement are used to produce various preconditioners of block triangular and block diagonal type. A few properties o...

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

In this paper we consider undirected graphs with no loops and multiple edges, consisting of k connected components. In these cases, it is well known that one can find a numbering of the vertices such that the adjacency matrix A is block diagonal with k blocks. This also holds for the (unnormalized) Laplacian matrix L = D − A, with D a diagonal matrix with the degrees of the nodes. In this paper...

It is shown that an innnite Hankel matrix of a nite rank (or a nite Hankel matrix) admits a generalized Vandermonde decomposition H = V T DV , where V is a generalized Vandermonde matrix, and D is a block diagonal matrix. The full structure of this decomposition was rst fully discussed by Vandevoorde 9], but the development here is based solely on linear algebra considerations, speciically the ...

In this paper we present a new robust adaptive algorithm. It is derived from the standard QR Decomposition based RLS (QRDRLS) algorithm by introducing a non-orthogonal transform into the update recursion. Instead of updating an upper triangular matrix, as it is the case for the QRD-RLS, we adapt an upper triangular block diagonal matrix. The complexity of the algorithm, thus obtained, varies fr...

Block Relative Gain (BRG) is a useful method for finding suitable pairings for block decentralized control. In this paper, we present some new algebraic properties of BRG and establish its relation with closed loop stability, controllability, block diagonal dominance and interactions. Contrary to published conjecture, we show that strongly interacting systems can have BRG that is nearly the ide...

There is normally a simple choice made in the form of the covariance matrix to be used with HMMs. Either a diagonal covariance matrix is used, with the underlying assumption that elements of the feature vector are independent, or a full or block-diagonal matrix is used, where all or some of the correlations are explicitly modelled. Unfortunately when using full or block-diagonal covariance matr...

In this paper we study algebraic sets of pairs matrices defined by the vanishing either diagonal their commutator matrix or its anti-diagonal. We find systems parameters for coordinate rings these two and intersection show that they are complete intersections. Moreover, prove F-pure over a field positive prime characteristic set with zero is F-regular.