We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $L^{N/2}(mathb...

We present an overview of the banded Invariant Subspace Decomposition Algorithm for symmetric matrices and describe a parallel implementation of this algorithm. The algorithm described here is a promising variant of the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA) that retains the property of using scalable primitives, while requiring signiicantly less overal...

In 1991, Sonnevend, Stoer, and Zhao [Math. Programming 52 (1991) 527–553] have shown that the central paths of strictly feasible instances of linear programs generate curves on the Grassmannian that satisfy a universal ordinary differential equation. Instead of viewing the Grassmannian Gr(m, n) as the set of all n×n projection matrices of rank m, we view it as the set R ∗ of all full column ran...

The computation of an enclosure for the solution of a sparse set of linear equations Ax = b with a thin matrix A and an interval right hand side b is considered. Gaussian elimination works well when the matrix is an M-matrix, but fails when the matrix is a general matrix. This paper illustrates how, for sparse matrices, an ordering intended to reduce the height of the elimination tree (and thus...

In the following, M,M denote respectively the set of all products of matrices in M, and the set of all products of length t of matrices in M. This problem is closely related to the so called joint spectral subradius of a set of matrices, which is the smallest asymptotic rate of growth of any long product of matrices in the set, when the length of the product increases. For a survey on the joint...

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...