When approximately calculating integrals of high dimension with the Monte Carlo method, one uses fewer values of the integrand than when calculating with the help of classical deterministic quadrature formulas.
interpreted in the sense of (1) toassign a sequence of expansion coefficients (Tf)(n) to each generalized functionf(x) in ’; the inverse transformation is obtained by summing the eigenfunctionexpansion in ’.In conclusion, the reviewer would like to make some comments of a moregeneral ...
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L. C. HsuL. W. LinKluwer Academic PublishersActa Mathematica Academiae Scientiarum HungaricaL. C. Hsu and L. W. Lin , Two new methods for the approximate calculation of multiple integrals, Acta Math. Acad. Sci. Hung. , 9 (1958), pp. 279–289....
Approximate evaluation of multiple integrals w.r.t. measures generated by multidimensional processes with independent increments are considered in Sections 8.3 and 8.4. This chapter derives a number of approximate formulae for functional integrals w.r.t. Gaussian measure....
Multiple integrals can be computed as iterated integrals, using the quadrature formulas described above. Since the number of nodes increases substantially with the multiplicity, a number of special formulas have been developed for the computation of multiple integrals. The calculation of integrals by ...
A quick calculation shows that for the given matrix A, pAx=x3−2x2−x+2=(x−2)(x−1)(x+1). Thus, λ1 = 2 is the dominant eigenvalue for A. Solving the system (2I3 −A)v = 0 produces an eigenvector v = [3,4,1] corresponding to λ1 = 2. Normalizing v yields ...
9See however [36, 37] for a calculation of an arbitrary point function. Note, however, that the individual weights of the operators are scaled in a particular way, such that ∆ ∼ ϵN , with ϵ → 0 and N →∞. –5– parameter space, sometimes referred to as "islands". ...
In principle, the calculation of the weights can be improved by considering more complex integrations over the gauge links as, for example: I2 = dU Tr [U v]a [U g]b Tr U † c ⎡ = ⎣∂xa ∂yb∂zc ∞ q =0 1 q!(q + 1)! x yTr g†v ⎤ + x zTr [v] + ...
Otadi, Gaussian quadratures for approximate of fuzzy multiple integrals, Applied Mathe- matics and Computation, 172 (2006) 175-187. https://doi.org/10.1016/j.amc.2005.01.135T. Allahviranloo and M. Otadi, "Gaussian quadratures for approximate of fuzzy multiple integrals," Applied Mathematics ...