<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e174" altimg="si232.svg"><mml:mi>H</mml:mi></mml:math>-sets for kernel-based spaces

The concept of H-sets as introduced by Collatz in 1956 was very useful univariate Chebyshev approximation polynomials or spaces. In the multivariate setting, situation is much worse, because there no alternation, and exist, but are only rarely accessible mathematical arguments. However, Reproducing Kernel Hilbert spaces, shown here to have a rather simple complete characterization. As byproduct, strong connection Linear Programming studied. But on downside, it explained why limited range applicability times large-scale computing.