Numerical analysis

Author: Chen Zengrong, edited by Gao Weiguo
Publisher:
Publish Date: 2002-05-01
Features: This book comprehensively and systematically introduces important algorithms in numerical analysis, along with a brief overview of floating-point computation, rounding error analysis, norms, the convergence and convergence rate of iterative methods, and the fundamental ideas and approaches for solving ordinary differential equations numerically. These basic principles hold significant importance in numerical analysis. When presenting algorithms, the book strives to make the content accessible, intentionally omitting complex and tedious theoretical proofs and derivations. The algorithms introduced primarily cover the following six aspects: solving function equations, direct and iterative methods for solving systems of linear algebraic equations, function interpolation, curve fitting, and function approximation, numerical integration, numerical solutions of ordinary differential equations, FFT transformations and their applications in image compression. Finally, the book introduces the basic concepts of parallel computing and fundamentals of programming. This book comprehensively and systematically introduces important algorithms in numerical analysis, along with a brief overview of floating-point computation, rounding error analysis, norms, the convergence and convergence rate of iterative methods, and the fundamental ideas and approaches for solving ordinary differential equations numerically. These basic principles hold significant importance in numerical analysis. When presenting algorithms, the book strives to make the content accessible, intentionally omitting complex and tedious theoretical proofs and derivations. The algorithms introduced primarily cover the following six aspects: solving function equations, direct and iterative methods for solving systems of linear algebraic equations, function interpolation, curve fitting, and function approximation, numerical integration, numerical solutions of ordinary differential equations, FFT transformations and their applications in image compression. Finally, the book introduces the basic concepts of parallel computing and fundamentals of programming. This book is suitable for senior undergraduate students and early-stage graduate students in computer science, electronic engineering, and other non-computational mathematics-related fields as a textbook or self-study reference.