This book is aimed at advanced undergraduate students and graduate students and is intended for a course in numerical analysis and approximation theory. The author covers topics such as multivariate interpolation, Peano kernel theory, and the applications of q-integers to approximation theory, the latter of which have never been fully examined in book form before.

Autorentext

George Phillips has lectured and researched in mathematics at the University of St. Andrews, Scotland. His most recent book, Two Millenia of Mathematics: From Archimedes to Gauss (Springer 2000), received enthusiastic reviews in the USA, Britain and Canada. He is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Klappentext

In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Inhalt

• Preface * Univariate Interpolation * Best Approximation * Numerical Integration * Peano's Theorem and Applications * Multivariate Interpolation * Splines * Bernstein Polynomials * Properties of the q-integers * References * Index *