Argyros I. Numerical Methods for Equations and its Applications 2012

Textbook in PDF format

This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis.
Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.
Newton's Method.
Secant Method.
Steffensen's Method.
Gauss–Newton Method.
Newton–type Methods.
Inexact Methods.
Werner's Method.
Halley's Method.
Methods for Variational Inequalities.
Fast Two–Step Methods.
Fixed Point Methods