2015_USTA_F_PhD.pdf (2.71 MB)
Sparse Grid Approximation with Gaussians
thesis
posted on 2015-10-15, 14:23 authored by Fuat UstaMotivated by the recent multilevel sparse kernel-based interpolation (MuSIK)
algorithm proposed in [Georgoulis, Levesley and Subhan, SIAM J. Sci. Comput.,
35(2), pp. A815-A831, 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 in comparison
with classical quasi-interpolation; namely, 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 quadrature
formula based on Q-MuSIK interpolation of the integrand. We present the
results of numerical experimentation for both interpolation and quadrature
in Rd, for d = 2, d = 3 and d = 4.
In this work we also consider the convergence rates for multilevel quasiinterpolation
of periodic functions using Gaussians on a grid. Initially, we
have given the single level quasi-interpolation error by using the shifting properties
of Gaussian kernel, and have then found an estimate for the multilevel
error using the multilevel algorithm for unit function.
History
Supervisor(s)
Levesley, Jeremy; Cangiani, AndreaDate of award
2015-10-01Author affiliation
Department of MathematicsAwarding institution
University of LeicesterQualification level
- Doctoral
Qualification name
- PhD