This book is a textbook for the course of "Numerical Analysis" generally offered in universities of science and engineering. Its contents include interpolation and approximation, numerical differentiation and numerical integration, numerical solution of nonlinear equations and linear equations, calculation of eigenvalues and eigenvectors of matrices, and numerical solution of ordinary differential equations. Each chapter is accompanied by exercises and some answers are given at the end of the book. Each chapter is also accompanied by review questions and calculation exercises. This book is rigorous, clear, simple and easy to teach. This book can also be used as a teaching material for graduate degree courses in universities of science and engineering, and can be used as a reference for scientific and technological workers engaged in scientific computing.

(1) simplifies some rarely used algorithms and some complicated derivation and proof in content; The analysis and explanation of the basic idea of the algorithm are strengthened. In addition, some new contents have been added, such as adaptive quadrature and calculation of multiple integrals, yoke gradient method for solving linear equations, ill-conditioned analysis for finding roots of algebraic equations, convergence and stability analysis of multi-step methods in numerical solutions of ordinary differential equations, and rigidity problems.

(2) Some explanations of historical development and the use of mathematical software are added in the commentary; Adding review and thinking questions in each chapter will help readers deepen their understanding of the basic content and promote the mastery of the algorithm; In addition, in order to strengthen the practice of using computers to solve problems, some calculation exercises have been added.

(3) According to the characteristics of the new edition of this book, the appendix of parallel algorithm is deleted. At present, there are many popular introductory works on parallel algorithms, and those who need to know can learn by themselves. In addition, this book recommends readers to use MATLAB language and math library, and this book does not introduce the use of MATLAB. At present, there are also many introduction books for reference.