Solving Grid Equations Using the Alternating-triangular Method on a Graphics Accelerator

A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions

a direct method for numerically solving integral equations system using orthogonal triangular functions

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Computational method based on triangular operational matrices for solving nonlinear stochastic differential equations

In this article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

a direct method for numerically solving integral equations system using orthogonal triangular functions

On the solving matrix equations by using the spectral representation

‎The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation‎. ‎We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A‎, ‎X in mathbb{C}^{n times n}$ and $b in mathbb{C} ^{n times s}$ with $s < n$‎, ‎which $X$ is unknown matrix‎. ‎Also‎, ‎we suggest the new method for solving quadratic matri...