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Higher order polynomial lattice point sets are special types of digital higher order nets which are known to achieve almost optimal convergence rates when used in a quasi-Monte Carlo algorithm to approximate high-dimensional integrals over the unit cube. Recently it has been shown that higher order polynomial lattice point sets of " good " quality must… (More)

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near optimal order of convergence. The main problem addressed in this paper is to find an efficient way of… (More)

In this paper we study an approximation algorithm which firstly approximates certain Walsh coefficients of the function under consideration and consequently uses a Walsh polynomial to approximate the function. A similar approach has previously been used for approximating periodic functions, using lattice rules (and Fourier polynomials), and for… (More)

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