Advisor(s) - Committee Chair
Dr. Mark Robinson (Director), Dr. Dominic Lanphier, and Dr. Ngoc Nguyen
Department of Mathematics
Master of Science
Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different acceleration techniques are discussed with analysis of the asymptotic behavior of the iterates. Analogies between single variable and multivariable problems are detailed. We also explore some interesting phenomena while analyzing Newton's method for complex variables.
Dynamical Systems | Non-linear Dynamics | Numerical Analysis and Computation
Alam, Md Shafiful, "Iterative Methods to Solve Systems of Nonlinear Algebraic Equations" (2018). Masters Theses & Specialist Projects. Paper 2305.