Topic
Inversive
About: Inversive is a research topic. Over the lifetime, 260 publications have been published within this topic receiving 2548 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: A new class of inversive congruential generators is introduced and it is shown that they have excellent statistical independence properties and model true random numbers very closely.
Abstract: Linear congruential pseudorandom numbers show several undesirable regularities which can render them useless for certain stochastic simulations. This was the motiviation for important recent developments in nonlinear congruential methods for generating uniform pseudorandom numbers. It is particularly promising to achieve nonlinearity by employing the operation of multiplicative inversion with respect to a prime modulus. In the present paper a new class of such inversive congruential generators is introduced and analyzed. It is shown that they have excellent statistical independence properties and model true random numbers very closely. The methods of proof rely heavily on Weil-Stepanov bounds for rational exponential sums. 39 refs.
84 citations
1 Jan 1998
TL;DR: A review of nonlinear methods for the generation of uniform pseudorandom numbers in the unit interval can be found in this paper, where the emphasis is on results of the theoretical analysis of quadratic congruential and (recursive) inversive generators, which are scattered over a fairly large number of articles.
Abstract: This review paper deals with nonlinear methods for the generation of uniform pseudorandom numbers in the unit interval. The emphasis is on results of the theoretical analysis of quadratic congruential and (recursive) inversive congruential generators, which are scattered over a fairly large number of articles. Additionally, empirical results of some sample generators in a two—level overlapping serial test are given.
83 citations
TL;DR: In this article, it was shown that inversive and divisive meadows of rational numbers can be obtained as initial algebras of finite equational specifications, and a simple constructions of variants of inversion-free meadows with a partial multiplicative inverse or division operation from inversion.
59 citations
56 citations
TL;DR: In this article, Dembowski and Hughes introduced the notion of locally projective-planar lattices, a general class of objects in which some properties particular to one or more of the above-mentioned planes are dispensed with.
Abstract: This investigation originated with a question about inversive planes, which was answered in [19] and [20]. Those results, as well as their analogues for Laguerre and Minkowski planes are special cases of the main result of the present paper; but we are now concerned with a more general class of objects here called "locally projective-planar lattices" in which some properties particular to one or more of the above-mentioned planes are dispensed with. Our main theorem will be introduced in Sect. 2; we begin here with some discussion of the classical examples. An inversive plane is an incidence structure (see Chap. II) ~ = (0, off) (elements of (g are called circles) which satisfies: (0) Circles are nonempty. (1) For each P~(9, ~p is an affine plane (where J e is the "internal" structure whose points are the points of (9 other than P, whose blocks are the circles of c~ which contain P, and whose incidence is that inherited from J ) . The order of J is the (common) order of the affine planes Jp . Inversive planes arise quite naturally in geometry in the following way. Let K be a skewfield and (9 an ovoid in PG(3, K). (I.e., (9 is a set of points satisfying: (1) no three points of (9 are collinear, and (2) if P~(9, then the union of all lines meeting (9 only in P is a plane. PG(3,K) denotes three-dimensional projective space over K.) Then the following incidence structure, ~r is an inversive plane: The points of J((9) are the points of (9. The circles of J((9) are those planes which meet (9 in more than one point. Incidence is inclusion. An inversive plane is said to be egglike 1 if is isomorphic to some J((9). * Supported in part by ONR Contract ~N00014-76-C-0366 1 This term is due to Dembowski and Hughes [131
55 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 6 |
| 2019 | 7 |
| 2018 | 6 |
| 2017 | 6 |
| 2016 | 5 |