TY - JOUR

T1 - A straightforward generalization of Diliberto and Straus' algorithm does not work

AU - Dyn, Nira

N1 - Funding Information:
* Sponsored by the United States Army under Contract DAAG29-75-C-0024. + On sabbatical at the Mathematics Research Center, University of Wisconsin-Madison.

PY - 1980/12

Y1 - 1980/12

N2 - An algorithm for best approximating in the sup-norm a function f ∈ C[0, 1]2 by functions from tensor-product spaces of the form πk ⊗ C[0, 1] + C[0, 1] ⊗ πl, 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, in general, converge for k2 + l2 > 0.

AB - An algorithm for best approximating in the sup-norm a function f ∈ C[0, 1]2 by functions from tensor-product spaces of the form πk ⊗ C[0, 1] + C[0, 1] ⊗ πl, 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, in general, converge for k2 + l2 > 0.

UR - http://www.scopus.com/inward/record.url?scp=33745427116&partnerID=8YFLogxK

U2 - 10.1016/0021-9045(80)90028-3

DO - 10.1016/0021-9045(80)90028-3

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AN - SCOPUS:33745427116

SN - 0021-9045

VL - 30

SP - 247

EP - 250

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 4

ER -