SOME ALGORITHMS OF THE BEST SIMULTANEOUS APPROXIMATION

Abstract

We consider various algorithms calculating best onesided simultaneous approximations. We assume that X is a compact subset of Rm satisfying X = intX, S is an n-dimensional subspace of C(X), and µ is any 'admissible' measure on X. For any l−tuple f1, · · · , f' in C(X), we present various ideas for best approximation to F from S(F ). The problem of best (both one and two-sided) approximation is a linear programming problem.

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