Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights

R Cools, F Kuo, D Nuyens, I Sloan - Mathematics of Computation, 2021 - ams.org
In a recent paper by the same authors, we provided a theoretical foundation for the
component-by-component (CBC) construction of lattice algorithms for multivariate $ L_2 …

Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters

R Cools, FY Kuo, D Nuyens… - 75 years of mathematics of …, 2020 - books.google.com
This paper provides the theoretical foundation for the construction of lattice algorithms for
multivariate L2 approximation in the worst case setting, for functions in a periodic space with …

Rank-1 lattice rules for multivariate integration in spaces of permutation-invariant functions: Error bounds and tractability

D Nuyens, G Suryanarayana, M Weimar - Advances in Computational …, 2016 - Springer
We study multivariate integration of functions that are invariant under permutations (of
subsets) of their arguments. We find an upper bound for the n th minimal worst case error …

Cubature formulas for multisymmetric functions and applications to stochastic partial differential equations

C Heitzinger, G Pammer, S Rigger - SIAM/ASA Journal on Uncertainty …, 2018 - SIAM
The numerical solution of stochastic partial differential equations and numerical Bayesian
estimation is computationally demanding. If the coefficients in a stochastic partial differential …

Efficient numerical integration of permutation-invariant functions

M Weimar - Numerical integration, integral equations and … - math.unipd.it
Motivated by problems from computational quantum physics we study the efficient numerical
integration of multivariate functions which are invariant under permutations (of subsets) of …