Interpolation and Approximation by Polynomials PDF

George-M Phillips

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 students understanding of the text.

6.1 Polynomial Interpolation We will begin by studying polynomials. There are several motivating factors for doing this: • Everyone is familiar with polynomials. • Polynomials can be easily and eﬃciently evaluated using Horner’s algorithm. • We may have heard of the Weierstrass Approximation Theorem which states that

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