Constructions of general polynomial lattice rules based on the weighted star discrepancy
نویسندگان
چکیده
منابع مشابه
Constructions of general polynomial lattice rules based on the weighted star discrepancy
In this paper we study construction algorithms for polynomial lattice rules over arbitrary polynomials. Polynomial lattice rules are a special class of digital nets which yield well distributed point sets in the unit cube for numerical integration. Niederreiter obtained an existence result for polynomial lattice rules over arbitrary polynomials for which the underlying point set has a small sta...
متن کاملGood lattice rules based on the general weighted star discrepancy
We study the problem of constructing rank-1 lattice rules which have good bounds on the “weighted star discrepancy”. Here the non-negative weights are general weights rather than the product weights considered in most earlier works. In order to show the existence of such good lattice rules, we use an averaging argument, and a similar argument is used later to prove that these lattice rules may ...
متن کاملThe construction of extensible polynomial lattice rules with small weighted star discrepancy
In this paper we introduce a construction algorithm for extensible polynomial lattice rules and we prove that the construction algorithm yields generating vectors of polynomials which are optimal for a range of moduli chosen in advance. The construction algorithm uses a sieve where the generating vectors are extended by one coefficient in each component at each step and where one keeps a certai...
متن کاملOn the Behavior of the Weighted Star Discrepancy Bounds for Shifted Lattice Rules
We examine the question of constructing shifted lattice rules of rank one with an arbitrary number of points n, an arbitrary shift, and small weighted star discrepancy. An upper bound on the weighted star discrepancy, that depends on the lattice parameters and is easily computable, serves as a figure of merit. It is known that there are lattice rules for which this upper bound converges as O(n−...
متن کاملTractability properties of the weighted star discrepancy
Tractability properties of various notions of discrepancy have been intensively studied in the last decade. In this paper we consider the so-called weighted star discrepancy which was introduced by Sloan and Woźniakowski. We show that under a very mild condition on the weights one can obtain tractability with s-exponent zero (s is the dimension of the point set). In the case of product weights ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2007
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2006.09.001