Abstract
The concept of H-sets as introduced by Collatz in 1956 was very useful in univariate Chebyshev approximation by polynomials or Chebyshev spaces. In the multivariate setting, the situation is much worse, because there is no alternation, and H-sets exist, but are only rarely accessible by mathematical arguments. However, in Reproducing Kernel Hilbert spaces, H-sets are shown here to have a rather simple and complete characterization. As a byproduct, the strong connection of H-sets to Linear Programming is studied. But on the downside, it is explained why H-sets have a very limited range of applicability in the times of large-scale computing.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.