Description
Book SynopsisThis book is intended for undergraduate and graduate researchers and practitioners in computational sciences and as a reference book for an advanced computational methods course. We have included new results for iterative procedures in abstract spaces general enough for handling inverse problems in various situations related to real-life problems through mathematical modeling. The book contains a plethora of updated bibliography and provides comparison between various investigations made in recent years in the field of computational mathematics in the wide sense. Iterative processes are the tools used to generate sequences approximating solutions of equations describing the real-life problems stated above and others originating from Biosciences, Engineering, Mathematical Economics, Mathematical Biology, Mathematical Chemistry, Mathematical Physics Medicine, Mathematical Programming, and other disciplines. The book also provides recent advancements on the study of iterative procedures and can be used as a source from which one can obtain the proper method to use in order to solve a problem. The book requires a fundamental background in Mathematical Statistics, Linear Algebra and Numerical Analysis. It may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences, Engineering and Computational Sciences.
Table of ContentsPrefaceMajorizing Sequences for Iterative Methods with ApplicationsOn a Fast Three Step Method for Solving Equations under Weak ConditionsBall Convergence of Two Derivative Free Iterative Methods for Solving Equations under Weak ConditionsQuasi-Newtonian Iterative ProcessesExtended Ball Convergence for a Chebyshev-Halley Family of Methods with One ParameterExtending the Applicability of Newtons Method under the Second Fr'echet-Derivative: Case IExtending the Applicability of Newtons Method Under the k-th (k≥2)Fr'echet Derivaitive: Case IIConvergence under w-Conditions and the k-Fr'echet Derivatives: Case IIIConvergence under w-Conditions on the Second Derivative: Case IVConvergence under Lipschitz Conditions: Case VConvergence under w-Lipschitz Conditions: Case VIConvergence of an Eight Order Four Step MethodA Fast Three Step MethodConvergence of a Method Using Derivatives and Divided DifferencesConvergence of a 2k MethodConvergence of an Eighth Order MethodConvergence for a Method Containing a Sum of Linear OperatorsLocal Convergence of a Two-Step Chebyshev-Type MethodLocal Convergence of a Three Parameter Sixth Order MethodLocal Convergence for a Steffensen-Type Method of Order EightConvergence of a Sixth Order MethodRoots of Polynomials and their ApplicationsHybrid High Convergence Order Iterative MethodsHybrid Newton-Like Methods with High Order of ConvergenceGlossary of Symbols.
