The Approximation of Functions: Linear theory |
Contents
CHAPTER ONE FUNDAMENTALS | 1 |
CHAPTER THREE | 52 |
CHAPTER FIVE THE WEIERSTRASS THEOREM | 94 |
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algorithm An(f approximation L(A approximation problem approximation theory approximation to f(x Assume assumption best approximation best L1-approximation best Tchebycheff approximation coefficients computational concludes the proof consider continuous function convex convex set defined degree of convergence denoted descent mapping determine deviation Dirichlet kernel En+1 error curve established F(Ak Fejér kernel finite number finite point set fm(x following theorem Fourier series g(Ak given hence Hölder condition implies interval kernel Kn(x L(Ak L(Am L(Ao L₁(f least-squares approximation Lemma Let f(x linear approximating function lowest point Lp-norm max f(x max L(A method of descent minimize nomials obtain orthogonal polynomials Padé table parameters plane of support Pn(x polynomial of degree R(Ak rational function result satisfies sequence sgn f(x sign function subset Tchebycheff norm Tchebycheff set Theorem 1-3 tion Tn(x transformation trigonometric sum unisolvent functions valid vector weight function Xn+1 zeros