Hilbert Spaces and Its Applications

Buch | Hardcover

244 Seiten

2021
Nova Science Publishers Inc (Verlag)
978-1-5361-8983-4 (ISBN)

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This book contains numerous selected contemporary topics, primarily in Hilbert space, although related extended material in Banach spaces and Riemannian manifolds is also included. A plethora of concrete problems from diverse disciplines are explored, such as: applied mathematics; mathematical biology; chemistry; economics; physics; scientific computing, and engineering. The solutions of such equations can only be found in closed form in special cases; this forces researchers and practitioners to focus on the development of iterative methods to generate a sequence converging to the solutions, provided that some convergence criteria depending on the initial data are satisfied. Due to the exponential development of technology, new iterative methods should be found to improve existing computers and create faster and more efficient ones. We have no doubt that this book will contribute significantly to the enrichment of knowledge and problem solving in the field of Hilbert spaces and related topics.

Preface; A Newton-Traub-Like Fifth Convergence Order Method in Hilbert Space; Correcting and extending the applicability of two fast algorithms for solving systems; Extended Directional Newton-Type Methods; Extended Kantorovich Theorem for Generalized Equations and Variational Inequalities; Extended the Applicability of Newtons Method for Equations with Monotone Operator; Improved Local Convergence for a Proximal Gauss-Newton Solver; Improved Error Estimates for Some Newton-type Methods; Two Non Classical Quantum Logic of Projections in Hilbert space; Extended Fourth Order Newton-Like Method under w-continuity for Solving Equations; On the semi-local convergence of Halleys method: An extension; Semi local convergence criterion of Newtons algorithm for singular systems under constant rank derivatives: An extension; Extending the Gauss-Newton-Algorithm under l-average continuity conditions; On the solution of generalized equations in Hilbert space; Newtons algorithm on Riemannian manifolds: Extended Kantorovichs theorem; Extended Gauss-Newton-Kurchatov Algorithm for least squares problems; Extended Gauss-Newton Algorithm for convex composite optimization; Extended local convergence of Newtons Algorithm on Riemannian manifolds; Uniqueness of the solution of equations in Hilbert space I; Uniqueness of the solution of equations in Hilbert space II; Extended Newtons Algorithm on Riemannian manifolds with values in a cone; Extended Gauss-Newton Algorithm on Riemannian manifolds under L- average Lipschitz conditions; New Results on Berezin Number Inequalities in Reproducing Kernel Hilbert Space; Glossary of Symbols; Index.

Erscheinungsdatum	25.02.2021
Sprache	englisch
Gewicht	460 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-5361-8983-9 / 1536189839
ISBN-13	978-1-5361-8983-4 / 9781536189834
Zustand	Neuware