Approximations for Digital Computers
Approximations for Digital Computers
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There has been a renewed interest of late in the problem of approximation in the Tchebycheff sense, that is of minimizing the maximum residues. Several methods 1, 2, 3, have already been discussed and many examples of approximating functions of one variable by polynomials and rational functions, etc. have been published. On the other hand the important problem of solving an overdetermined system of linear equations in the Tchebycheff sense has not been given the attention it deserves. The possession of a practical method for the solution of this problem would make possible “best” approximations of functions of several variables by linear combinations of arbitrary functions. It is not widely known that an algorithm for solving this problem exists and is due to de la Vallee Poussin.4 Unfortunately the algorithm is unwieldy but it is still useful in the computation of a minimum approximation. We shall therefore outline the results of de la Vallee Poussin before discussing some new methods with which we have been experimenting.