## On numerical approximation: proceedings of a symposium conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison, April 21-23, 1958 |

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### Contents

On Trends and Problems in Numerical Approximation | 3 |

Linear Spaces and Approximation Theory | 11 |

Operational Methods in Numerical Analysis Based on Rational | 25 |

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Akad Amer analytic functions apply approximate f assume asymptotic Bernstein Bernstein polynomials best approximation coefficients computation confluent forms confluent limits consider constant continuous functions convergent convex corresponding defined denote differential equation divided difference Dokl E. T. Whittaker element error bound example exists finite func function F Gaussian given function Hilbert space implies inequality interpolation formulas interval kernel Lemma linear combination linear functionals linear space linearly independent lower bound Math method minimizing minimum error Nauk SSSR N.S. norm Numerical Analysis obtained operator optimal orthogonal orthogonal polynomials periodic functions Pn(x points polynomial approximation polynomial of degree problem proof quadratic quadratic form reference representation Russian satisfied scheme sequence solution subspace Taylor series Theorem theory tion transformation trapezoidal rule unique values variables variation diminishing zeros