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- Fred J. Hickernell
- Math. Comput.
- 1998

An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, whichâ€¦ (More)

The Halton sequence is a well-known multi-dimensional low discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence: we randomize the start point of eachâ€¦ (More)

- Fred J. Hickernell, Harald Niederreiter
- J. Complexity
- 2003

Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there existâ€¦ (More)

- Fred J. Hickernell, Henryk Wozniakowski
- Adv. Comput. Math.
- 2000

We study multivariate integration in the worst case setting and multivariate approximation in the average case setting for various classes of functions of d variables with arbitrary d. We considerâ€¦ (More)

Abstract. Good lattice quadrature rules are known to have O(N) convergence for periodic integrands with sufficient smoothness. Here it is shown that applying the bakerâ€™s transformation to latticeâ€¦ (More)

- Keqin Feng, Lanju Xu, Fred J. Hickernell
- Finite Fields and Their Applications
- 2006

A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography. Thisâ€¦ (More)

We prove that for the space of functions with mixed first derivatives bounded in L1 norm, the weighted integration problem over bounded or unbounded regions is equivalent to the correspondingâ€¦ (More)

- Fred J. Hickernell
- ACM Trans. Model. Comput. Simul.
- 1996

One popular family of low dicrepancy sets is the (<italic>t, m, s</italic>)-nets. Recently a randomization of these nets that preserves their net property has been introduced. In this article aâ€¦ (More)

- Hee Sun Hong, Fred J. Hickernell
- ACM Trans. Math. Softw.
- 2003

Random scrambling of deterministic (t, m, s)-nets and (t, s)-sequences eliminates their inherent bias while retaining their low-discrepancy properties. This article describes an implementation of twoâ€¦ (More)

- Ben Niu, Fred J. Hickernell, Thomas MÃ¼ller-Gronbach, Klaus Ritter
- J. Complexity
- 2011

Pricing a path-dependent financial derivative, such as an Asian option, requires the computation of E(g(B)), the expectation of a payoff function g , that depends on a Brownian motion B. Employing aâ€¦ (More)