Contemporary Algorithms: Theory and Applications Volume II

$230.00

Christopher I. Argyros – Researcher, Department of Computing and Mathematical Sciences, Cameron University, Lawton, Oklahoma, USA
Samundra Regmi – Researcher, Learning Commons, University of North Texas at Dallas, Dallas, TX, USA
Ioannis K. Argyros, PhD – Professor, Department of Computing and Mathematical Sciences, Cameron University, Lawton, Oklahoma, USA
Santhosh George, PhD – Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, India

Series: Mathematics Research Developments
BISAC: MAT003000; MAT027000
DOI: 10.52305/ZTPR4079

The book is a continuation of Volume I with the same title. It provides different avenues to study algorithms. It also brings new techniques and methodologies to problem solving in computational sciences, engineering, scientific computing and medicine (imaging, radiation therapy) to mention a few. A plethora of algorithms are presented in a sound analytical way. The chapters are written independently of each other, so they can be understood without reading earlier chapters. But some knowledge of analysis, linear algebra, and some computing experience are required. The organization and content of the book cater to senior undergraduate, graduate students, researchers, practitioners, professionals, and academicians in the aforementioned disciplines. It can also be used as a reference book and includes numerous references and open problems.

Table of Contents

Preface

Chapter 1. Correcting and Extending the Applicability of Two Fast Algorithms
1. Introduction
2. Semi-Local Convergence
3. Conclusion

Chapter 2. On the Solution of Generalized Equations in Hilbert Space
1. Introduction
2. Convergence
3. Numerical Examples
4. Conclusion

Chapter 3. Gauss-Newton Algorithm for Convex Composite Optimization
1. Introduction
2. Convergence of GNA
3. Conclusion

Chapter 4. Local Convergence of Newton’s Algorithm of Riemannian Manifolds
1. Introduction
2. Convergence
3. Conclusion

Chapter 5. Newton’s Algorithm on Riemannian Manifolds with Values in a Cone
1. Introduction
2. Semi-Local Convergence
3. Conclusion

Chapter 6. Gauss-Newton Algorithm on Riemannian Manifolds under L-Average Lipschitz Conditions
1. Introduction
2. Semi-Local Convergence
3. Conclusion

Chapter 7. Newton’s Method with Applications to Interior Point Algorithms of Mathematical Programming
1. Introduction
2. An Improved Newton–Kantorovich Theorem
3. Applications to Interior-Point Algorithm
4. Conclusion

Chapter 8. Newton’s Method for Solving Nonlinear Equations Using Generalized Inverses: Part I Outer Inverses
1. Introduction
2. Convergence
3. Conclusion

Chapter 9. Newton’s Method for Solving Nonlinear Equations Using Generalized Inverses: Part II Matrices
1. Introduction
2. Local Convergence
3. Conclusion

Chapter 10. Newton’s Method for Solving Nonlinear Equations Using Generalized Inverses: Part III Ball of Convergence for Nonisolated Solutions
1. Introduction
2. Convergence of Method (10.2)
3. Conclusion

Chapter 11. On an Efficient Steffensen-Like Method to Solve Equations
1. Introduction
2. Analysis
3. Conclusion

Chapter 12. Convergence Analysis for King-Werner-Like Methods
1. Introduction
2. Semi-Local Convergence of Method (12.2)
3. Local Convergence of Method (12.2)
4. Numerical Examples
5. Conclusion

Chapter 13. Multi-Point Family of High Order Methods
1. Introduction
2. Local Convergence
3. Numerical Examples
4. Conclusion

Chapter 14. Ball Convergence Theorems for Some Third-Order Iterative Methods
1. Introduction
2. Local Convergence for Method (14.2)
3. Local Convergence of Method (14.3)
4. Numerical Examples
5. Conclusion

Chapter 15. Convergence Analysis of Frozen Steffensen-Type Methods under Generalized Conditions
1. Introduction
2. Semi-Local Convergence Analysis
3. Conclusion

Chapter 16. Convergence of Two-Step Iterative Methods for Solving Equations with Applications
1. Introduction
2. Semi-Local Convergence Analysis
3. Local Convergence Analysis
4. Numerical Examples
5. Conclusion

Chapter 17. Three Step Jarratt-Type Methods under Generalized Conditions
1. Introduction
2. Local Analysis
3. Numerical Examples
4. Conclusion

Chapter 18. Extended Derivative Free Algorithms of Order Seven
1. Introduction
2. Local Analysis
3. Numerical Examples
4. Conclusion

Chapter 19. Convergence of Fifth OrderMethods for Equations under the Same Conditions
1. Introduction
2. Local Convergence
3. Numerical Examples
4. Conclusion

Chapter 20. A Novel Eighth Convergence Order Scheme with Derivatives and Divided Difference
1. Introduction
2. Convergence
3. Numerical Examples
4. Conclusion

Chapter 21. Homocentric Ball for Newton’s and the Secant Method
1. Introduction
2. Local Convergence
3. Semi-Local Convergence
4. Numerical Examples
5. Conclusion

Chapter 22. A Tenth Convergence Order Method under Generalized Conditions
1. Introduction
2. Convergence
3. Numerical Examples
4. Conclusion

Chapter 23. Convergence of Chebyshev’s Method
1. Introduction
2. Semi-Local Convergence Analysis
3. Local Convergence Analysis
4. Numerical Experiments
5. Conclusion

Chapter 24. Gauss-Newton Algorithms for Optimization Problems
1. Introduction
2. Convergence
3. Conclusion

Chapter 25. Two-Step Methods under General Continuity Conditions
1. Introduction
2. Majorizing Sequences
3. Semi-Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 26. A Noor-Waseem Third Order Method to Solve Equations
1. Introduction
2. Majorizing Sequences
3. Semi-Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 27. Generalized Homeier Method
1. Introduction
2. Local Convergence
3. Numerical Experiments
4. Conclusion

Chapter 28. A Xiao-Yin Third Order Method for Solving Equations
1. Introduction
2. Majorizing Sequences
3. Semi-Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 29. Fifth Order Scheme
1. Introduction
2. Scalar Sequences
3. Semi-Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 30. Werner Method
1. Introduction
2. Majorizing Sequences
3. Semi-Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 31. Yadav-Singh Method of Order Five
1. Introduction
2. Semi-Local Convergence
3. Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 32. Convergence of a P+1 Step Method of Order 2P+1 with Frozen Derivatives
1. Introduction
2. Local Convergence
3. Numerical Experiments
4. Conclusion

Chapter 33. Efficient Fifth Order Scheme
1. Introduction
2. Ball Convergence
3. Numerical Experiments
4. Conclusion

Chapter 34. Sharma-Gupta Fifth Order Method
1. Introduction
2. Convergence
3. Numerical Experiments
4. Conclusion

Chapter 35. Seventh Order Method for Equations
1. Introduction
2. Convergence
3. Numerical Experiments
4. Conclusion

Chapter 36. Newton-Like Method
1. Introduction
2. Mathematical Background
3. Majorizing Sequences
4. Semi-Local Convergence
5. Numerical Experiments
6. Conclusion

Chapter 37. King-Type Methods
1. Introduction
2. Majorizing Sequences
3. Semi-Local Convergence
4. Numerical Experiments
5. Conclusion

Chapter 38. Single Step Third Order Method
1. Introduction
2. Semi-Local Analysis
3. Local Convergence
4. Numerical Example
5. Conclusion

Chapter 39. Newton-Type Method for Non-Differentiable Inclusion Problems
1. Introduction
2. Majorizing Sequences
3. Analysis
4. Conclusion

Chapter 40. Extended Kantorovich-Type Theory for Solving Nonlinear Equations Iteratively: Part I Newton’s Method
1. Introduction
2. Convergence of NM
3. Conclusion

Chapter 41. Extended Kantorovich-Type Theory for Solving Nonlinear Equations Iteratively: Part II Newton’s Method
1. Introduction
2. Convergence of NLM
3. Conclusion

Chapter 42. Updated and Extended Convergence Analysis for Secant-Type Iterations
1. Introduction
2. Convergence of STI
3. Conclusion

Chapter 43. Updated Halley’s and Chebyshev’s Iterations
1. Introduction
2. Semi-Local Convergence Analysis for HI and CI
3. Conclusion

Chapter 44. Updated Iteration Theory for Non Differentiable Equations
1. Introduction
2. Convergence
3. Conclusion

Chapter 45. On Generalized Halley-Like Methods for Solving Nonlinear Equations
1. Introduction
2. Majorizing Convergence Analysis
3. Semi-Local Analysis
4. Special Cases
5. Conclusion

Chapter 46. Extended Semi-Local Convergence of Steffensen-Like Methods for Solving Nonlinear Equations
1. Introduction
2. Majorizing Real Sequences
3. Convergence
4. Conclusion

Glossary of Symbols

Index