A Straightforward Generalization of Diliberto and Straus' Algorithm Does Not Work.

摘要

An algorithm for best approximation in the sup-norm a function f an element of C(0,1)-squared by functions from tensor-product spaces of the form pi sub k x C(0,1) x C(0,1) x pi sub l, is considered. For the case k=l=0 the Diliberto and Straus algorithm is known to converge. A straightforward generalization of this algorithm to general k,l is formulated, and an example is constructed demonstrating that this algorithm does not converge for K-squared + l-squared > 0. (Author)