Research in Mathematics at Cameron University

Ioannis K Argyros (Autor)

Buch | Hardcover

421 Seiten

2021
Nova Science Publishers Inc (Verlag)
978-1-5361-9417-3 (ISBN)

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Numerous problems from diverse disciplines can be converted using mathematical modelling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or 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 optimised 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.

Ioannis K. Argyros was born in 1956 in Athens, Greece. He received a B.Sc. from the University of Athens, Greece; and a M.Sc. And Ph.D. from the University of Georgia, Athens, Georgia, USA, under the supervision of Dr. Douglas N. Clark. Dr. Argyros is currently a full Professor of Mathematics at Cameron University, Lawton, OK, USA. His research interests include: Applied mathematics, Operator theory, Computational mathematics and iterative methods especially on Banach spaces. He has published more than a thousand peer reviewed papers, thirty two books and seventeen chapters in books in his area of research, computational mathematics. He is an active reviewer of a plethora of papers and books, and has received several national and international awards. He has supervised two PhD students, several MSc. and undergraduate students, and has been the external evaluator for many PhD theses, tenure and promotion applicants.

Preface; Author Contact Information; The History of Newtons Method and Extended Classical Results; Extended Global Convergence of Iterative Methods; Extended Gauss-Newton-Approximate Projection Methods of Constrained Nonlinear Least Squares Problems; Convergence Analysis of Inexact Gauss-Newton Like for Solving Systems; Local Convergence of the Gauss-Newton Scheme on Hilbert Spaces Under a Restricted Convergence Domain; Ball Convergence for Inexact Newton-type Conditional Gradient Solver for Constrained Systems; Newton-like Methods with Recursive Approximate Inverses; Updated Mesh Independence Principle; Ball Convergence for Ten Solvers Under the Same Set of Conditions; Extended Newtons Solver for Generalized Equations Using a Restricted Convergence Domain; Extended Newtons Method for Solving Generalized Equations: Kantorovichs Approach; Extended Robust Convergence Analysis of Newtons Method for Cone Inclusion Problems in Banach Spaces; Extended and Robust Kantorovichs Theorem on the Inexact Newtons Method with Relative Residual Error Tolerance; Extended Local Convergence for Iterative Schemes Using the Gauge Function Theory; Improved Local Convergence of Inexact Newton Methods under Average Lipschitz-type Conditions; Semi-Local Convergence of Newtons Method Using the Gauge Function Theory: An Extension; Extending the Semi-Local Convergence of Newtons Method Using the Gauge Theory; Global Convergence for Chebyshevs Method; Extended Convergence of Efﬁcient King-Werner-Type Methods of Order 1+√2; Extended Convergence for Two Chebyshev-Like Methods; Extended Convergence Theory for Newton-Like Methods of Bounded Deterioration; Extending the Kantorovich Theorem for Solving Equations Using Telescopic Series; Extended ω-Convergence Conditions for the Newton-Kantorovich Method; Extended Semilocal Convergence Analysis for Directional Newton Method; Extended Convergence of Damped Newtons Method; Extended Convergence Analysis of a One-Step Intermediate Newton Iterative Scheme for Nonlinear Equations; Enlarging the Convergence Domain of Secant-Type Methods; Two-Step Newton-Type Method for Solving Equations; Two-Step Secant-Type Method for Solving Equations; Uniﬁed Convergence for General Iterative Schemes; Extending the Applicability of Gauss-Newton Method for Convex Composite Optimization; Local Convergence Comparison Between Newtons and the Secant Method: Part-I; Convergence Comparison Between Newtons and Secant Method: Part-II; Extended Convergence Domains for a Certain Class of Fredholm Hammerstein Equations; Extended Convergence of the Gauss-Newton-Kurchatov Method; Extended Semi-Local Convergence of Newtons Method under Conditions on the Second Derivative; Extended Convergence for the Secant Method Under Mysovskii-like Conditions; Glossary of Symbols.

Erscheinungsdatum	28.04.2021
Sprache	englisch
Maße	155 x 230 mm
Gewicht	696 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-5361-9417-4 / 1536194174
ISBN-13	978-1-5361-9417-3 / 9781536194173
Zustand	Neuware