Abstract
We introduce a new notion of tractability for multivariate problems, namely (s,lnκ)-weak tractability for positive s and κ. This allows us to study the information complexity of a d-variate problem with respect to different powers of d and the bits of accuracy lnε−1. We consider the worst case error for the absolute and normalized error criteria. We provide necessary and sufficient conditions for (s,lnκ)-weak tractability for general linear problems and linear tensor product problems defined over Hilbert spaces. In particular, we show that non-trivial linear tensor product problems cannot be (s,lnκ)-weakly tractable when s∈(0,1] and κ∈(0,1]. On the other hand, they are (s,lnκ)-weakly tractable for κ>1 and s>1 if the univariate eigenvalues of the linear tensor product problem enjoy a polynomial decay. Finally, we study (s,lnκ)-weak tractability for the remaining combinations of the values of s and κ.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
