Applied Mathematical Methods

43

Minimax Approximation*

In several chapters all over this book, we have considered various ways and means of representation and approximation of functions. There remains one more important mode of approximation, the minimax approximation or Chebyshev approximation, which is taken up in the present chapter. First, we examine Chebyshev polynomials and their unique properties to recognize the character of Chebyshev series approximation. Next, we discuss the notions and construction of general minimax polynomial approximation.

Approximation with Chebyshev polynomials

Through the exercises in Chaps. 39 and 40, the reader has already collected some information on Chebyshev polynomials. Let us first supplement that information with additional aspects ...