This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on one or several parameters. Specifically, we consider the situation when the parameter dependence is sufficiently smooth and the aim is to compute solutions for many different parameter samples. Based on existing results for Lyapunov...

Problems involving estimation and inference under linear inequality constraints arise often in statistical modeling. In this paper we propose an algorithm to solve the quadratic programming problem of minimizing ψ(θ) = θ′Qθ−2c′θ for positive-definite Q, where θ is constrained to be in a closed polyhedral convex cone C = {θ : Aθ ≥ d}, and the m×n matrix A is not necessarily full row-rank. The th...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

R. A. Fisher's 1930 "reproductive value" is defined as the contribution made by a population's initial age elements to its asymptotically dominating exponential growth mode. For the Leslie discrete-time model, it is the characteristic row vector of the Leslie matrix, and for the integral-equation model of Lotka the similar eigenfunction. It generalizes neatly to a 2-sex model of linear differen...

We consider the solution of a linear system Ax = b on a distributedmemorymachine when the matrixA has full rank and is large, sparse and nonsymmetric. We use our Cartesian nested dissection algorithm to compute a ll-reducingcolumn ordering of the matrix. We develop algorithms that use the associated separator tree to estimate the structure of the factor and to distribute and perform numeric com...

encryption is an important tool for managing and protecting information. cryptography is the only practical means of sending information over an insecure channel. these channels may be computers, telephone lines, satellite, etc. the increasing use of electronic means of data transfer from one point to another, coupled with the growth in networking and internet communication, has extended the ne...

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.