Beschreibung:
This book covers the main topics concerned with interpolation and approximation by polynomials. This subject can be traced back to the precalculus era but has enjoyed most of its growth and development since the end of the nineteenth century and is still a lively and flourishing part of mathematics. 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.
This book is aimed at advanced undergraduate students and graduatestudents and is intended for a course in numerical analysis andapproximation theory. The author covers topics such as multivariateinterpolation, Peano kernel theory, and the applications of q-integersto approximation theory, the latter of which have never been fullyexamined in book form before.
Univariate Interpolation.- Best Approximation.- Numerical Integration.- Peano's Theorem and Applications.- Multivariate Interpolation.- Splines.- Bernstein Polynomials.- Properties of the q-Integers.