TY - JOUR
T1 - An Algorithm-Driven Approach to Error Analysis for Multidimensional Integration
AU - F. J. Hickernell & J. Dick
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 167
EP - 189
PY - 2008
DA - 2008/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/805.html
KW - digital nets, integration lattices, randomized, worst-case.
AB - <p style="text-align: justify;">Most error analyses for numerical integration algorithms
specify the space of integrands and then determine the convergence rate
for a particular algorithm or the optimal algorithm. This article takes
a different perspective of specifying the convergence rate and then
finding the largest space of integrands for which the algorithm gives
that desired rate. Both worst-case and randomized error analyses are
provided.</p>