Usta, FuatLevesley, Jeremy2020-04-302020-04-3020181017-13981572-9265https://doi.org/10.1007/s11075-017-0340-yhttps://hdl.handle.net/20.500.12684/3747Levesley, Jeremy/0000-0002-3509-0152WOS: 000425616500008Motivated by the recent multilevel sparse kernel-based interpolation (MuSIK) algorithm proposed in Georgoulis et al. (SIAM J. Sci. Comput. 35, 815-832, 2013), we introduce the new quasi-multilevel sparse interpolation with kernels (Q-MuSIK) via the combination technique. The Q-MuSIK scheme achieves better convergence and run time when compared with classical quasi-interpolation. Also, the Q-MuSIK algorithm is generally superior to the MuSIK methods in terms of run time in particular in high-dimensional interpolation problems, since there is no need to solve large algebraic systems. We subsequently propose a fast, low complexity, high-dimensional positive-weight quadrature formula based on Q-MuSIKSapproximation of the integrand. We present the results of numerical experimentation for both quasi-interpolation and quadrature in high dimensions.en10.1007/s11075-017-0340-yinfo:eu-repo/semantics/closedAccessQuasi-interpolationMultilevelSparse gridsHyperbolic crossesQuadratureHigh dimensionArticle773793808WOS:000425616500008Q2Q1