New Developments of Newton-Type Iterations for Solving Nonlinear Problems

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.

• 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.