2019/01/17 by Rong Guo, Heping Wang, Guo, Rong +1
Mathematics · #Mathematical Approximation and Integration #Mathematical functions and polynomials #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.1901.05752
We study multivariate linear tensor product problems with some special properties in the worst case setting. We consider algorithms that use finitely many continuous linear functionals. We use a unified method to investigate tractability of the above multivariate problems, and obtain necessary and sufficient conditions for strong polynomial tractability, polynomial tractability, quasi-polynomial tractability, uniformly weak tractability, (s,t)-weak tractability, and weak tractability. Our results can apply to multivariate approximation problems with kernels corresponding to Euler kernels, Wiener kernels, Korobov kernels, Gaussian kernels, and analytic Korobov kernels.