Solving interpolation problems on surfaces stochastically and greedily

TitleSolving interpolation problems on surfaces stochastically and greedily
Publication TypeJournal Article
Year of Publication2022
AuthorsChen, M, Ling, L, Su, Y
JournalDolomites Research Notes on Approximation
Date Published10/2022
PublisherPadova University Press
Place PublishedPadova, IT
ISSN Number2035-6803

Choosing suitable shape parameters in the kernel-based interpolation problems is an open question, whose solutions can guarantee accuracy and numerical stability. In this paper, we study various ways to select Kernel’s shape parameters for interpolation problems on surfaces. In particular, we use exact and stochastically approximated cross validation approaches to select the shape parameters. When we solve the resultant matrix systems, we also deploy a greedy trial subspace selection algorithm to improve robustness. Numerical experiments are inserted along our discussion to demonstrate the feasibility and robustness of our proposed methods.