FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1964669306> ?p ?o ?g. }

• W1964669306 endingPage "467" @default.
• W1964669306 startingPage "443" @default.
• W1964669306 abstract "In this paper we study lattice rules which are cubature formulae to approximate integrands over the unit cube [0,1] s from a weighted reproducing kernel Hilbert space. We assume that the weights are independent random variables with a given mean and variance for two reasons stemming from practical applications: (i) It is usually not known in practice how to choose the weights. Thus by assuming that the weights are random variables, we obtain robust constructions (with respect to the weights) of lattice rules. This, to some extend, removes the necessity to carefully choose the weights. (ii) In practice it is convenient to use the same lattice rule for many different integrands. The best choice of weights for each integrand may vary to some degree, hence considering the weights random variables does justice to how lattice rules are used in applications. In this paper the worst-case error is therefore a random variable depending on random weights. We show how one can construct lattice rules which perform well for weights taken from a set with large measure. Such lattice rules are therefore robust with respect to certain changes in the weights. The construction algorithm uses the component-by-component (cbc) idea based on two criteria, one using the mean of the worst case error and the second criterion using a bound on the variance of the worst-case error. We call the new algorithm the cbc2c (component-by-component with 2 constraints) algorithm. We also study a generalized version which uses r constraints which we call the cbcrc (component-by-component with r constraints) algorithm. We show that lattice rules generated by the cbcrc algorithm simultaneously work well for all weights in a subspace spanned by the chosen weights γ (1), . . . , γ (r). Thus, in applications, instead of finding one set of weights, it is enough to find a convex polytope in which the optimal weights lie. The price for this method is a factor r in the upper bound on the error and in the construction cost of the lattice rule. Thus the burden of determining one set of weights very precisely can be shifted to the construction of good lattice rules. Numerical results indicate the benefit of using the cbc2c algorithm for certain choices of weights." @default.
• W1964669306 created "2016-06-24" @default.
• W1964669306 creator A5004856556 @default.
• W1964669306 date "2012-04-04" @default.
• W1964669306 modified "2023-09-23" @default.
• W1964669306 title "Random weights, robust lattice rules and the geometry of the cbcrc algorithm" @default.
• W1964669306 cites W134944766 @default.
• W1964669306 cites W1480319329 @default.
• W1964669306 cites W1543280314 @default.
• W1964669306 cites W1590281894 @default.
• W1964669306 cites W1820164671 @default.
• W1964669306 cites W1981743146 @default.
• W1964669306 cites W1986280275 @default.
• W1964669306 cites W1989439787 @default.
• W1964669306 cites W2002243597 @default.
• W1964669306 cites W2011200438 @default.
• W1964669306 cites W2015558767 @default.
• W1964669306 cites W2025580195 @default.
• W1964669306 cites W2032381682 @default.
• W1964669306 cites W2035455944 @default.
• W1964669306 cites W2036346468 @default.
• W1964669306 cites W2040396531 @default.
• W1964669306 cites W2042083287 @default.
• W1964669306 cites W2047549016 @default.
• W1964669306 cites W2053270912 @default.
• W1964669306 cites W2059141990 @default.
• W1964669306 cites W2092528496 @default.
• W1964669306 cites W2094952117 @default.
• W1964669306 cites W2166634029 @default.
• W1964669306 cites W2497677836 @default.
• W1964669306 cites W598051755 @default.
• W1964669306 doi "https://doi.org/10.1007/s00211-012-0469-5" @default.
• W1964669306 hasPublicationYear "2012" @default.
• W1964669306 type Work @default.
• W1964669306 sameAs 1964669306 @default.
• W1964669306 citedByCount "4" @default.
• W1964669306 countsByYear W19646693062013 @default.
• W1964669306 countsByYear W19646693062014 @default.
• W1964669306 countsByYear W19646693062016 @default.
• W1964669306 countsByYear W19646693062017 @default.
• W1964669306 crossrefType "journal-article" @default.
• W1964669306 hasAuthorship W1964669306A5004856556 @default.
• W1964669306 hasBestOaLocation W19646693062 @default.
• W1964669306 hasConcept C105795698 @default.
• W1964669306 hasConcept C11413529 @default.
• W1964669306 hasConcept C114614502 @default.
• W1964669306 hasConcept C121332964 @default.
• W1964669306 hasConcept C122123141 @default.
• W1964669306 hasConcept C134306372 @default.
• W1964669306 hasConcept C24890656 @default.
• W1964669306 hasConcept C2781204021 @default.
• W1964669306 hasConcept C33923547 @default.
• W1964669306 hasConcept C62799726 @default.
• W1964669306 hasConceptScore W1964669306C105795698 @default.
• W1964669306 hasConceptScore W1964669306C11413529 @default.
• W1964669306 hasConceptScore W1964669306C114614502 @default.
• W1964669306 hasConceptScore W1964669306C121332964 @default.
• W1964669306 hasConceptScore W1964669306C122123141 @default.
• W1964669306 hasConceptScore W1964669306C134306372 @default.
• W1964669306 hasConceptScore W1964669306C24890656 @default.
• W1964669306 hasConceptScore W1964669306C2781204021 @default.
• W1964669306 hasConceptScore W1964669306C33923547 @default.
• W1964669306 hasConceptScore W1964669306C62799726 @default.
• W1964669306 hasIssue "3" @default.
• W1964669306 hasLocation W19646693061 @default.
• W1964669306 hasLocation W19646693062 @default.
• W1964669306 hasOpenAccess W1964669306 @default.
• W1964669306 hasPrimaryLocation W19646693061 @default.
• W1964669306 hasRelatedWork W1482827353 @default.
• W1964669306 hasRelatedWork W1973606933 @default.
• W1964669306 hasRelatedWork W1978042415 @default.
• W1964669306 hasRelatedWork W1980535956 @default.
• W1964669306 hasRelatedWork W2017331178 @default.
• W1964669306 hasRelatedWork W2046162582 @default.
• W1964669306 hasRelatedWork W2157453222 @default.
• W1964669306 hasRelatedWork W2976797620 @default.
• W1964669306 hasRelatedWork W3086542228 @default.
• W1964669306 hasRelatedWork W3096340483 @default.
• W1964669306 hasVolume "122" @default.
• W1964669306 isParatext "false" @default.
• W1964669306 isRetracted "false" @default.
• W1964669306 magId "1964669306" @default.
• W1964669306 workType "article" @default.