Tractability of Integration in Non-periodic and Periodic Weighted Tensor Product Hilbert Spaces
Copyright policy )Tractability of Integration in Non-periodic and Periodic Weighted Tensor Product Hilbert Spaces
The authors study strong tractability and tractability of multivariate integrals in weighted tensor product reproducing kernel Hilbert spaces. They obtain necessary and sufficient conditions on strong tractability and tractability in terms of the weights of the space. For the three Sobolev spaces periodicity has no significant effect on strong tractability and tractability (section 2) but the general reproducing kernel Hilbert spaces we may have strong tractability or tractability for the non-periodic case and intertractability for the periodic one (section 3, section 4 and section 5).
- UNSW Sydney Australia
- University of Warsaw Poland
Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Applied Mathematics, Multidimensional problems, Monte Carlo methods, periodic function, Sobolev space, Numerical quadrature and cubature formulas, multivariate integrals, Approximate quadratures, tractability, intractability, weighted tensor product reproducing kernel Hilbert spaces, strong tractability
Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Applied Mathematics, Multidimensional problems, Monte Carlo methods, periodic function, Sobolev space, Numerical quadrature and cubature formulas, multivariate integrals, Approximate quadratures, tractability, intractability, weighted tensor product reproducing kernel Hilbert spaces, strong tractability
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