Open Science Research Excellence

Davod Khojasteh Salkuyeh

Publications

2

Publications

2
11434
Stepsize Control of the Finite Difference Method for Solving Ordinary Differential Equations
Abstract:

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.

Keywords:
Ordinary differential equations, optimal stepsize, error, stochastic arithmetic, CESTAC, CADNA.
1
14436
Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems
Abstract:
We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.
Keywords:
rank deficient least squares problems, AOR iterativemethod, Gauss-Seidel iterative method, semiconvergence.