This comprehensive book delves into the intricacies of Newton-type methods for nonlinear equations, offering insights into their convergence, accelerations, and extensions. Divided into three parts, the book explores higher-order iterations for nonlinear equations and their systems, and their applications in linear algebra and some nonlinear problems of theoretical physics. Emphasizing the pivotal role of iteration parameters in shaping convergence and expanding the domain, the authors draw from their extensive collaborative research to systematically compile and elucidate these findings. Catering to readers, graduate students, and researchers in applied mathematics, numerical analysis, and related disciplines, this book serves as a valuable resource, synthesizing decades of research to advance understanding and practical application in the field

Newton-type methods rely heavily on carefully chosen iteration parameters It not only accelerates convergence and expands the convergence domain but also enables the control convergence behavior It compile these advancements for researchers in applied mathematics, numerical analysis, and applied sciences

Autorentext

Academician Tugal Zhanlav's research interests lie in computational mathematics, with a focus on wavelet analysis, spline approximations, numerical methods for linear algebra problems, iterative methods for solving nonlinear systems, and the convergence and stability of finite-difference schemes. Academician Tugal Zhanlav has authored or co-authored over 150 scientific publications. Academician Ochbadrakh Chuluunbaatar is a computational physicist with expertise in mathematical modeling, variational methods, and numerical approaches for solving few-body problems. His research focuses on high-precision calculations in quantum mechanics, particularly the energy states of multielectron atoms and molecules, multichannel scattering problems, and ionization behavior under particle impact. Academician Ochbadrakh Chuluunbaatar has authored or co-authored over 230 scientific publications and contributed to the development of valuable computing programs in the field of computational physics.

Inhalt

Part 1. Newton-Type Iterations for Nonlinear Equations.- 1. Newton-Type Iterations, Convergence and Accelerations.- 2. Two-Sided Approximations.- 3. New Developments and Extensions of Newton-Type Methods.- 4. Derivative-Free Iterative Methods.- Part 2. Higher Order Iterations for Systems of Nonlinear Equations.- 5. Higher Order Newton-Type Iterations.- Part 3. Applications.- 6. Newton-Type Iterations for Solving Some Problems in Linear Algebra.