The ultimate aim of the field of numerical analysis is to provide
convenient methods for obtaining useful solutions to mathematical
problems and for extracting useful information from available solutions
which are not expressed in tractable forms. This well-known, highly
respected volume provides an introduction to the fundamental processes
of numerical analysis, including substantial grounding in the basic
operations of computation, approximation, interpolation, numerical
differentiation and integration, and the numerical solution of
equations, as well as in applications to such processes as the smoothing
of data, the numerical summation of series, and the numerical solution
of ordinary differential equations.
Chapter headings include:
l. Introduction
2. Interpolation with Divided Differences
3. Lagrangian Methods
4. Finite-Difference Interpolation
5. Operations with Finite Differences
6. Numerical Solution of Differential Equations
7. Least-Squares Polynomial Approximation
In this revised and updated second edition, Professor Hildebrand
(Emeritus, Mathematics, MIT) made a special effort to include more
recent significant developments in the field, increasing the focus on
concepts and procedures associated with computers. This new material
includes discussions of machine errors and recursive calculation,
increased emphasis on the midpoint rule and the consideration of Romberg
integration and the classical Filon integration; a modified treatment of
prediction-correction methods and the addition of Hamming's method, and
numerous other important topics.
In addition, reference lists have been expanded and updated, and more
than 150 new problems have been added. Widely considered the classic
book in the field, Hildebrand's Introduction to Numerical Analysis is
aimed at advanced undergraduate and graduate students, or the general
reader in search of a strong, clear introduction to the theory and
analysis of numbers.
