Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume III



Series: Mathematics Research Developments
BISAC: MAT027000

These books are intended for undergraduate, graduate researchers and practitioners in computational sciences, and as reference books 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. These books contain a plethora of updated bibliography and provide 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.

These books also provide, 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 books require 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.
(Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Local Convergence for a Family of Super-Halley Methods

Chapter 2. A Unified Local Convergence Analysis of Newton-Like Methods

Chapter 3. Ball Convergence Theorems for Fourth-Order Variants of Newton’s Method

Chapter 4. Local Convergence Theorems for Some Third and Fourfth Order Methods

Chapter 5. Ball Convergence of Potra-Ptak-Type Method

Chapter 6. Householder-Type Iterative Free from Second Derivative

Chapter 7. Convergence for a Newton-Jarratt-Like Composition

Chapter 8. Convergence for a Novel Iterative Method Free from the Second Derivative

Chapter 9. Ball Convergence Theorems for Fourth-Order Variants of Newton’s Method

Chapter 10. J. Chen’s One Step Third-Order Iterative Methods

Chapter 11. Ball Convergence for a Sixteenth Order Iterative Methods

Chapter 12. Convergence for a Jarratt-Like Method for Solving Equations

Chapter 13. Convergence of a Sixth Order Ostrowski-Like Method for Solving Equations

Chapter 14. Convergence for a Householder-Like Method

Chapter 15. Local Convergence of the Two-Step Chebyshev-Like Method

Chapter 16. Comparison between Two Sixth Order Newton-Jarratt Method

Chapter 17. Newton’s Method Using Gauss-Legendre Formulas

Chapter 18. Composite Newton-Traub Method

Chapter 19. Convergence of a Four Step Ninth Order Method

Chapter 20. Convergence of an Eighth-Order Method in Banach Space

Chapter 21. Convergence for a General Family of Optimal Fourth-Order Methods

Chapter 22. Gauss-Newton Method Using Restricted Convergence Domains

Chapter 23. Proximal Gauss-Newton Method Using Restricted Convergence Domains

Chapter 24. Hybrid High Convergence Order Iterative Methods

Chapter 25. High Convergence Order Methods on Riemannian Manifolds

Chapter 26. Convergence Analysisconvergence Analysis of a Muller Secant-Type Method

Chapter 27. Convergence of Bilinear Operator

Chapter 28. Convergence Analysis for Semi-Smooth Newton-Type Methods

Chapter 29. Hybrid High Convergence Order Iterative Methods

Chapter 30. the King-Werner Method of Order

Chapter 31. Extending the Applicability of King-Werner-Type Methods

Chapter 32. Achieving Higher Order of Convergence for Solving Systems of Equations

Chapter 33. Gauss-Newton Method for Convex Composite Optimization

Chapter 34. High Order Method Based on the Decomposition Technique

Chapter 35. Kantorovich-Type Extensions for Newton Method

Chapter 36. Divided Difference-Based Iterative Methods

Chapter 37. Convergence for the Osada Method

Chapter 38. Convergence for Newton-Kantorovich-Like Theorems

Chapter 39. Unified Convergence of Fourth Order Solvers

Chapter 40. Extending the Kantorovich Theorem

Chapter 41. Two-Step Iterative Methods Free of Derivatives

Chapter 42. Inexact Newton-Type Methods

Chapter 43. Ball Convergence Theorems for Fourth-Order Variants of Newton’s Method


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