We consider a family of symmetric matrices A! = A 0 + !B; with a nonnegative deenite matrix A 0 ; a positive deenite matrix B; and a nonnegative parameter ! 1: Small ! leads to a poor conditioned matrix A! with jumps in the coeecients. For solving linear algebraic equations with the matrix A!; we use standard preconditioned iterative methods with the matrix B as a preconditioner. We show that a...

Continuity properties of factors in polar decompositions of matrices with respect to inde®nite scalar products are studied. The matrix having the polar decomposition and the inde®nite scalar product are allowed to vary. Closely related properties of a self-adjoint (with respect to an inde®nite scalar product) perturbed matrix to have a self-adjoint square root, or to have a representation of th...

Three simple mesh examples are presented to show that neither Delaunay nor strictly non-obtuse mesh elements are required for a nite element computation. Mesh requirements based on a recent condition given in literature are investigated to guarantee certain properties of the resulting stiiness matrix. The experiments are conducted using a general nite element and nite volume solver.

Introduction: Highly active antiretroviral therapy (HAART) has improved outcomes for individuals infected with human immunodefi ciency virus (HIV). This study describes the causes of death in hospitalised HIV-positive patients from 2008 to 2010 in Tan Tock Seng Hospital, the national referral centre for HIV management in Singapore. Materials and Methods: Data were retrospectively collected from...

Compared to artificial metamaterials, where nano-fabrication complexities and finite-size inclusions can hamper the desired electromagnetic response, several natural materials like van der Waals crystals hold great promise for designing efficient nanophotonic devices in optical range. Here, we investigate unusual response of NiTe$_2$, a crystal type-II Dirac semimetal hosting Lorentz-violating ...

Inversion of a triangular matrix can be accomplished in several ways. The standard methods are characterised by the loop ordering, whether matrix-vector multiplication, solution of a triangular system, or a rank-1 update is done inside the outer loop, and whether the method is blocked or unblocked. The numerical stability properties of these methods are investigated. It is shown that unblocked ...

We show that Jacobi's method (with a proper stopping criterion) computes small eigenvalues of symmetric positive de nite matrices with a uniformly better relative accuracy bound than QR, divide and conquer, traditional bisection, or any algorithm which rst involves tridiagonalizing the matrix. In fact, modulo an assumption based on extensive numerical tests, we show that Jacobi's method is opti...

This paper presents a new computational method for steady state analysis of nite QBD-process with level-dependent transitions. The QBD state space is deened in two-dimension with N phases and K levels. Instead of formulating solutions in matrix-geometric form, the Folding-algorithm provides a technique for direct computation of P = 0, where P is the QBD generator which is an (NK)(NK) matrix. Ta...

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.