Hilbert Spaces and Its Applications


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Series: Mathematics Research Developments

BISAC: MAT012000

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.


Table of Contents


Chapter 1: A Newton-Traub-Like Fifth Convergence Order Method in Hilbert Space
Chapter 2: Correcting and extending the applicability of two fast algorithms for solving systems
Chapter 3: Extended Directional Newton-Type Methods
Chapter 4: Extended Kantorovich Theorem for Generalized Equations and Variational Inequalities
Chapter 5: Extended the Applicability of Newton’s Method for Equations with Monotone Operator
Chapter 6: Improved Local Convergence for a Proximal Gauss-Newton Solver
Chapter 7: Improved Error Estimates for Some Newton-type Methods
Chapter 8: Two Non Classical Quantum Logic of Projections in Hilbert space
Chapter 9: Extended Fourth Order Newton-Like Method under w-continuity for Solving Equations
Chapter 10: On the semi-local convergence of Halley’s method: An extension
Chapter 11: Semi local convergence criterion of Newton’s algorithm for singular systems under constant rank derivatives: An extension
Chapter 12: Extending the Gauss-Newton-Algorithm under l-average continuity conditions
Chapter 13: On the solution of generalized equations in Hilbert space
Chapter 14: Newton’s algorithm on Riemannian manifolds: Extended Kantorovich’s theorem
Chapter 15: Extended Gauss-Newton-Kurchatov Algorithm for least squares problems
Chapter 16: Extended Gauss-Newton Algorithm for convex composite optimization
Chapter 17: Extended local convergence of Newton’s Algorithm on Riemannian manifolds
Chapter 18: Uniqueness of the solution of equations in Hilbert space: I
Chapter 19: Uniqueness of the solution of equations in Hilbert space: II
Chapter 20: Extended Newton’s Algorithm on Riemannian manifolds with values in a cone
Chapter 21: Extended Gauss-Newton Algorithm on Riemannian manifolds under L- average Lipschitz conditions
Chapter 22: New Results on Berezin Number Inequalities in Reproducing Kernel Hilbert Space

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