Undergraduate Research at Cameron University on Iterative Procedures in Banach and Other Spaces

Ioannis K. Argyros and Samundra Regmi
Cameron University, Department of Mathematical Sciences, Lawton, Oklahoma, USA

Series: Mathematics Research Developments
BISAC: MAT003000

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This 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.
(Imprint: Nova)

Preface

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Chapter 1. Majorizing Sequences for Iterative Methods with Applications

Chapter 2. On a Fast Three Step Method for Solving Equations under Weak Conditions

Chapter 3. Ball Convergence of Two Derivative Free Iterative Methods for Solving Equations under Weak Conditions

Chapter 4. Quasi-Newtonian Iterative Processes

Chapter 5. Extended Ball Convergence for a Chebyshev-Halley Family of Methods with One Parameter

Chapter 6. Extending the Applicability of Newton’s Method under the Second Fr´echet-Derivative: Case I

Chapter 7. Extending the Applicability of Newton’s Method Under the k-th (k≥ 2)Fr´echet Derivaitive: Case II

Chapter 8. Convergence under w-Conditions and the k-Fr´echet Derivatives: Case III

Chapter 9. Convergence under w-Conditions on the Second Derivative: Case IV

Chapter 10. Convergence under Lipschitz Conditions: Case V

Chapter 11. Convergence under w-Lipschitz Conditions: Case VI

Chapter 12. Convergence of an Eight Order Four Step Method

Chapter 13. A Fast Three Step Method

Chapter 14. Convergence of a Method Using Derivatives and Divided Differences

Chapter 15. Convergence of a 2k Method

Chapter 16. Convergence of an Eighth Order Method

Chapter 17. Convergence for a Method Containing a Sum of Linear Operators

Chapter 18. Local Convergence of a Two-Step Chebyshev-Type Method

Chapter 19. Local Convergence of a Three Parameter Sixth Order Method

Chapter 20. Local Convergence for a Steffensen-Type Method of Order Eight

Chapter 21. Convergence of a Sixth Order Method

Chapter 22. Roots of Polynomials and their Applications

Chapter 23. Hybrid High Convergence Order Iterative Methods

Chapter 24. Hybrid Newton-Like Methods with High Order of Convergence

Glossary of Symbols

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