A typical first step of a direct solver for the linear system Mx = b is reordering of the symmetric matrix M to improve execution time and space requirements of the solution process. In this work, we propose a novel nested-dissection-based ordering approach that utilizes hypergraph partitioning. Our approach is based on the formulation of graph partitioning by vertex separator (GPVS) problem as...

In this study, the changes in microstructure of HP-Nb cast heat resistant steel after 8 years of service at high temperatures were investigated. Study of microstructure using optical microscopy (OM) and scanning electron microscopy (SEM) equipped with an energy dispersive spectrometry (EDS) showed that the microstructure of this steel in as-cast condition includes an austenitic matrix, and that...

This is sometimes called the Netflix problem. A motivation for the matrix completion problem comes from user ratings of some products which are put into a matrix M . The entries Mij of the matrix correspond to the j’th user’s rating of product i. We assume that there exists an ideal matrix that encodes the ratings of all the products by all the users. However, it is not possible to ask every us...

The spectrum of a matrix M is the multiset that contains all the eigenvalues of M. If M is a matrix obtained from a graph G, then the spectrum of M is also called the graph spectrum of G. If two graphs has the same spectrum, then they are cospectral (or isospectral) graphs. In this paper, we compare four spectra of matrices to examine their accuracy in protein structural comparison. These four ...

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obta...

Let A be a nonsingular M -matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M -matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M -matrix A. Numerical examples show that the results obtained are an improvement over ...

Let A be a nonsingular M -matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M -matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M -matrix A. Numerical examples show that the results obtained are an improvement over ...