Using a finite number of additions, subtractions, multiplications, and comparisons, the only functions of one variable that one can compute are piece-wise polynomials. If we add division to the set of available operations, the only functions one can compute are piecewise rational functions. Therefore it is natural to try to approximate the elementary functions by polynomials or rational functions. Throughout this chapter we denote by P n the set of the polynomials of degree less than or equal to n, and by R p,q the set of the rational functions whose numerator and denominator have degrees less than p and q, respectively.
KeywordsTaylor Expansion Rational Approximation Polynomial Approximation Chebyshev Polynomial Chebyshev Approximation
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