47 citations · 411 across the 42 of their papers we have counts for
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Constructing good higher order polynomial lattice rules with modulus of reduced degree
Takashi Goda
In this paper we investigate multivariate integration in weighted unanchored Sobolev spaces of smoothness of arbitrarily high order. As quadrature points we employ higher order pol…
Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces
Takashi Goda
Quadrature rules using higher order digital nets and sequences are known to exploit the smoothness of a function for numerical integration and to achieve an improved rate of conver…
Fast construction of higher order digital nets for numerical integration in weighted Sobolev spaces
Takashi Goda
Higher order digital nets are special classes of point sets for quasi-Monte Carlo rules which achieve the optimal convergence rate for numerical integration of smooth functions. An…
Construction of interlaced scrambled polynomial lattice rules of arbitrary high order
Takashi Goda, Josef Dick
Higher order scrambled digital nets are randomized quasi-Monte Carlo rules which have recently been introduced in [J. Dick, Ann. Statist., 39 (2011), 1372--1398] and shown to achie…
On the separability of multivariate functions
Takashi Goda
Separability of multivariate functions alleviates the difficulty in finding a minimum or maximum value of a function such that an optimal solution can be searched by solving severa…
Construction of scrambled polynomial lattice rules over with small mean square weighted discrepancy
Takashi Goda
The discrepancy is one of several well-known quantitative measures for the equidistribution properties of point sets in the high-dimensional unit cube. The concept…