Abstract
In this paper we discuss estimation of the quasi-Monte Carlo methods error in the case of calculation of high-order integrals. Quasi-random Halton sequences are considered as a special case. Randomization of these sequences by the random shift method turns out to lead to well-known random quadrature formulas with one free node. Some new properties of such formulas are pointed out. The subject is illustrated by a number of numerical examples.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 17-01-00267-a
Funding statement: This work was partially supported by the Russian Foundation for Basic Research, Project No. 17-01-00267-a.
References
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