EXTENDING THE SOLVABILITY OF EQUATIONS USING SECANT-TYPE METHODS IN BANACH SPACE

Abstract

We extend the solvability of equations defined on a Banach space using numerically efficient secant-type methods.The convergence domain of these methods is enlarged using our new idea of restricted convergence region. By using this approach, we obtain a more precise location where the iterates lie than in earlier studies leading to tighter Lipschitz constants. This way the semi-local convergence produces weaker sufficient convergence criteria and tighter error bounds than in earlier works. These improvements are also obtained under the same computational effort, since the new Lipschitz constants are special cases of the old ones. © 2021, Publishing House of the Romanian Academy. All rights reserved.