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The book is a continuation of Volume I with the same title. It provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms are presented in a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience are required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems.
A new technique is developed to extend the convergence region and provide tighter error estimates of Newton’s Algorithm (NA) for solving generalized equations for Hilbert space- valued operators without additional conditions. The technique is very general, so it can be used to extend the applicability of other algorithms too.
The goal of this chapter is to present a unified local convergence analysis of frozen Steffensen-type methods under generalized Lipschitz-type conditions for Banach space-valued operators. We also use our new idea of restricted convergence domains, where we find a more precise __cpLocation where the iterates lie leading to at least as tight majorizing functions. Consequently, the new convergence criteria are weaker than in earlier works resulting in the expansion of the applicability of these methods. The conditions do not necessarily imply the differentiability of the operator involved. This way, our method is suitable for solving equations and systems of equations. The problem of locating a zero x∗ of the operator F is very important in many diverse areas such as inverse theory, optimization, control theory, Mathematical Physics, Chemistry, Biology, Economics, Computational Sciences, and also in Engineering