Optimized Iterative Methods with Applications in Diverse Disciplines


Samundra Regmi (Author) – Independent Researcher and Professional Mathematics Tutor, Learning Commons, University of North Texas at Dallas, Dallas, TX, USA

Series: Mathematics Research Developments

BISAC: MAT000000

Numerous problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space, Hilbert space, Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use iterative algorithms, which seem to be the only alternative.

Due to the explosion of technology, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. That is exactly where we come in with our book containing such algorithms with applications in problems from numerical analysis and economics but also from other areas such as biology, chemistry, physics, parallel computing, and engineering. The book is an outgrowth of scientific research conducted over two years.

This book can be used by senior undergraduate students, graduate students, researchers, and practitioners in the aforementioned areas in the classroom or as reference material. Readers should know the fundamentals of numerical-functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to readers.

Table of Contents


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Chapter 1. Oligopoly

Chapter 2. Extended Recurrence Relations for Newton-Type Method

Chapter 3. A Kantorovich-type Extension for the Inexact Newton Method

Chapter 4. Extended Gauss-Newton Method for Convex Composite Optimization

Chapter 5. Extended Two Step Fourth Order Method

Chapter 6. Extended Semi-local Convergence for a Super-Halley-Type Method for Fourth Order

Chapter 7. Semi-local Convergence of a Deformed Euler-Halley Method

Chapter 8. Deformed Halley Method for Solving Equations

Chapter 9. Extended Semilocal Convergence for Chebyshev-Like Methods

Chapter 10. Extended Local Convergence for a Chebyshev-Halley-Chun Method

Chapter 11. Extended Local Convergence for a Chebyshev-Halley-Chun II Method

Chapter 12. Extended Multipoint Jarratt Method

Chapter 13. Local Convergence for a Chebyshev-Like Method Free of Bilinear Operator

Chapter 14. Extended Local Convergence for a Jarratt-Type Method

Chapter 15. Local Convergence for a Fourth Order Method with Banach Space Valued Operators

Chapter 16. Local Convergence Analysis of a Fourth Order Method II with Banach Space Valued Operators

Chapter 17. Local Convergence Analysis of Fourth Order Methods III with Banach Space Valued Operators

Chapter 18. Local Convergence for a Two-Step Method Free of Derivative

Chapter 19. Two-Step Method with Five Parameters

Chapter 20. On a Jarratt-Type Three-Step Method

Chapter 21. Extended Semi-local Convergence of Halley’s Method

Chapter 22. Extended Newton-type Methods on Riemannian Manifolds for Determining a Singularity of a Vector Field

Chapter 23. Extended Smale’s α-Theory for Inexact Newton Method and the Gamma Condition

Chapter 24. Extended Semi-local Convergence for a Deformed Newton’s Method of Third Order and the Gamma Condition

Chapter 25. Extended Chebyshev-type Method

Chapter 26. Extended Convergence for a Class of High Order Methods

Chapter 27. Newton-type Method Under Uniform Convergence Conditions

Chapter 28. On a Two Step Third Order Solver

Chapter 29. Extended Convergence of Halley’s Method under Kantorovich’s Majorants

Chapter 30. Solution of Polynomial Equations Using Newton’s Method

Glossary of Symbols

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