SENSITIVITY OF SOME STATIONARY ITERATIVE METHODS TO TOLERANCE PARAMETER
A. A. Ibrahimand R. O. Osinowo
Department of Mathematical Sciences,
Oduduwa University, Ipetumodu, Ile-Ife, Nigeria
Email: adebisiibrahim97@gmail.com
ABSTRACT
Stationary iterative solution of algebraic system of equations requires the input of the coefficient matrix , the constant column vector , the initial approximation , the tolerance parameter, and , the intended maximum number of iterations.. While the coefficient matrix and the column vector are given, the initial approximation, usually taken to be the zero column vector of the same dimension as the constant column vector , the tolerance parameter and the intended maximum iterations are to be supplied by the one performing the operation. Again, the intended maximum iterations only sets the limit that must not be exceeded, the tolerance parameter plays a significant role in the arithmetic precision of the output. The Jacobi and the Gauss-Seidel iterations are used to solve some equations and they yielded useful results. The tolerance parameter was observed to have effect on the number of iterations as well as their minimization of the errors involved.
Keywords: Stationary iterative methods, algebraic system of equations, tolerance parameter, minimization of the errors.
