Analysis of Some Nonstationary Iterative Methods Using the Pascal and Vandermonde Linear Systems

Abstract

In this paper, analysis of some nonstationary iterative methods using the Vandermonde and Pascal linear system is reported. The nonstationary iterative methods selected were GMRES and QMR to assess their performance on the identified linear systems. The paper focused on the convergence relative residual and number of iteration for each type of chosen linear system. The Vandermonde matrix is mostly applied to interpolation of both quadratic and cubic polynomial function. The resulting polynomial has the form: p(x) = a_n xⁿ + a_n-1x^n-1 +...+ a₁x + a₀. From the numerical experiments conducted using the matlab programming language, the GMRES is recommended when solving the identified linear systems.