This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents relatively few theorems and proofs. Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency, and it compares different solutions to the same problem.Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms, interpolation, numerical differentiation and numerical quadrature, the numerical solution of ordinary differential equations, functional approximation by least squares and by minimum-maximum error techniques, the solution of nonlinear equations and of simultaneous linear equations, and the calculation of eigenvalues and eigenvectors of matrices.This second edition also includes discussions of spline interpolation, adaptive integration, the fast Fourier transform, the simplex method of linear programming, and simple and double QR algorithms. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
Anthony Ralston Book order (chronological)
The fourth edition of this handbook provides explanations of the technology of the late 1990s and its applications, including past, present and predicted future trends in computer science. The work has been completely revised and updated to reflect developments in computer science and technology since publication of the third edition in 1992. Arranged alphabetically, the 660 entries are also classified into sections covering the main themes of computing: hardware, software, computer graphics, information and data, mathematics of computing, methodologies, applications and computing milieu.
Jedná se o první větší soustavný výklad o numerické matematice. Svým obsahem pokrývá všechny metody matematické analýzy a algebry.