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 -