James M. Ortega 
Numerical Analysis [PDF ebook] 
A Second Course

Computer Science and Applied Mathematics: Numerical Analysis: A Second Course presents some of the basic theoretical results pertaining to the three major problem areas of numerical analysis-rounding error, discretization error, and convergence error. This book is organized into four main topics: mathematical stability and ill conditioning, discretization error, convergence of iterative methods, and rounding error. In these topics, this text specifically discusses the systems of linear algebraic equations, eigenvalues and eigenvectors, and differential and difference equations. The discretization error for initial and boundary value problems, systems of linear and nonlinear equations, and rounding error for Gaussian elimination are also elaborated. This publication is recommended for undergraduate level students and students taking a one-semester first-year graduate course for computer science and mathematics majors.