An efficient numerical method is developed for evaluating φ(A), where A is a symmetric matrix and φ is the function defined by φ(x) = (ex − 1)/x = 1+ x/2 + x2/6+ .... This matrix function is useful in the so-called exponential integrators for differential equations. In particular, it is related to the exact solution of the ODE system dy/dt = Ay + b, where A and b are t-independent. Our method a...

Consider a matrix with positive diagonal entries, which is similar via a positive diagonal matrix to a symmetric matrix, and whose signed directed graph has the property that if a cycle and its symmetrically placed complement have the same sign, then they are both positive. We provide sufficient conditions so that A be a P–matrix, that is, a matrix whose principal minors are all positive. We fu...

An n×n matrix is called an N1 0 -matrix if all its principal minors are non-positive and each entry is non-positive. In this paper, we study general combinatorially symmetric partial N1 0 -matrix completion problems and prove that a combinatorially symmetric partial N1 0 -matrix with all specified offdiagonal entries negative has an N1 0 -matrix completion if the graph of its specified entries ...

In this paper, we propose the use of complex-orthogonal transformations for nding the eigenvalues of a complex symmetric matrix. Using these special transformations can signiicantly reduce computational costs because the tridiagonal structure of a complex symmetric matrix is maintained.

The electron states in axially symmetric quantum wires are computed by means of the effective mass Schrodinger equation, which is written in cylindrical coordinates \phi, \rho, and z. We show that a direct discretization of the Schrodinger equation by central finite differences leads to a nonsymmetricHamiltonian matrix. Because diagonalization of such matrices is more complex it is advantageous...

An n × n matrix is called an N0-matrix if all its principal minors are nonpositive. In this paper, we are interested in N0-matrix completion problems, that is, when a partial N0-matrix has an N0-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N0-matrix does not have an N0-matrix completion. Here, we prove that a combinatorially symmetric partial N0-matr...

Vol. 9 No. 1 1997 27 In computing, a cluster is loosely defined as a parallel system comprising a collection of stand-alone computers (each called a node) connected by a network. Each node runs its own copy of the operating system, and cluster software coordinating the entire parallel system attempts to provide users with a unified system view. Since each node in the cluster is an off-the-shelf...