## Approximation of functions: theory and numerical methods |

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### Contents

Linear Approximation | 1 |

3 General Theory of Linear Tchebycheff Approximation | 13 |

Estimating the Magnitude of Error in Trigonometric and Polynomial | 45 |

Copyright | |

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### Common terms and phrases

analytic functions approximation of f(x approximation problem assertion assume assumption asymptotically convex best approximation coefficients Collatz consider continuous function convergence corresponding denote derivative differentiable dimension entire functions error function example exists a number extremal points Fejer operator finite formula Fourier series function f(x Haar condition Hence holomorphic functions hypotheses implies inequality initial approximation integer interval 1,1 iteration method Kolmogoroff Korovkin linear functional linear space linear subspace lower bound Meinardus modulus of continuity monotone N. I. Achieser norm obtain parameter partial sum polynomial approximation polynomials of degree possesses prescribed proof of Theorem rational approximation rational functions real interval regularity ellipse Remez algorithm Rolle's theorem S. N. Bernstein satisfies the Haar Schwedt sequence set M0 sufficiently Suppose the function system of equations Tchebycheff polynomials Theorem 58 Theorem 76 Theorem 85 trigonometric sum vanishes vector Weierstrass xeMa zeros