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Volume 5, Issue 2
An Algorithm-Driven Approach to Error Analysis for Multidimensional Integration

F. J. Hickernell & J. Dick

Int. J. Numer. Anal. Mod., 5 (2008), pp. 167-189.

Published online: 2008-05

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  • Abstract

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.

  • Keywords

digital nets, integration lattices, randomized, worst-case.

  • AMS Subject Headings

65D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-167, author = {F. J. Hickernell and J. Dick}, title = {An Algorithm-Driven Approach to Error Analysis for Multidimensional Integration}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {2}, pages = {167--189}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/805.html} }
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 -

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.

F. J. Hickernell and J. Dick. (2008). An Algorithm-Driven Approach to Error Analysis for Multidimensional Integration. International Journal of Numerical Analysis and Modeling. 5 (2). 167-189. doi:
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