A Quadratically Convergent Class of Modifications for Kovarik's Method

Abstract

In this article, a single parametric class of modifications for Kovarik's method is proposed. It is proved that all methods in this class are quadratically convergent. Numerical comparison among methods of Kovarik, Petcu-Popa [5], and a special method in this class, chosen based on a specific value for the parameter, shows that Kovarik and Petcu-Popa's methods give almost similar convergence results. However, the special method converges faster and its iteration number is considerably lower than that of others. For Numerical experiments, there are used ten $n\times n$ test matrices with $n=5,10,20,50$, whose condition numbers vary in the interval [$2\,,\,8.1e146$].