SUMMARY This issue contains papers dealing with a variety of linear and nonlinear matrix equations arising in systems and control theory, model reduction, and in various other areas of applied mathematics, economics, engineering, and the sciences. Special emphasis is given to the numerical treatment of large-scale problems. This special issue of Numerical Linear Algebra with Applications is dev...

Referring to one of the recent works of the authors, presented in~cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangula...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

This paper is concerned with numerical solutions to general linear matrix equations including the wellknown Lyapunov matrix equation and Sylvester matrix equation as special cases. Gradient based iterative algorithm is proposed to approximate the exact solution. A necessary and sufficient condition guaranteeing the convergence of the algorithm is presented. A sufficient condition that is easy t...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...

Motivated by a recent result of Elberfeld, Jakoby and Tantau[EJT10] showing that MSO properties are Logspace computable on graphs of bounded tree-width, we consider the complexity of computing the determinant of the adjacency matrix of a bounded tree-width graph and as our main result prove that it is in Logspace. It is important to notice that the determinant is neither an MSO-property nor cou...

‎in this paper, we study some kinds of majorizations on $textbf{m}_{n}$ and their linear or strong linear preservers. also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $phi $ with the property $phi (ab)=phi (a)phi (b)$ for every $a,bin textbf{m}_{n}$.

This equation may be viewed as reducing the sum of n terms of the power sequence to a linear combination of the first r + 1 terms. Accordingly, there is an implicit assumption that n > v. Note that the matrix appearing as the middle factor on the right side of this equation is lower triangular. The zeros that should appear above the main diagonal have been omitted. The nonzero entries constitut...