
Random Number Generators on Computers
Jenny Stanford Publishing
1st Edition
Published on 28. November 2024
Book
Hardback
110 pages
978-981-4968-49-2 (ISBN)
Description
This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1,z1) and (d2,z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2,z) with high probability by Sunzi's theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2,z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi's theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.
More details
Language
English
Place of publication
Singapore
Target group
College/higher education
Professional and scholarly
Academic and Postgraduate
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 11 mm
Weight
339 gr
ISBN-13
978-981-4968-49-2 (9789814968492)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Naoya Nakazawa | Hiroshi Nakazawa
Random Number Generators on Computers
E-Book
11/2024
1st Edition
Pan Stanford Publishing Pte Ltd
€101.99
Available for download

Naoya Nakazawa | Hiroshi Nakazawa
Random Number Generators on Computers
E-Book
11/2024
1st Edition
Pan Stanford Publishing Pte Ltd
€101.99
Available for download
Persons
Naoya Nakazawa obtained his DSci (applied number theory) at Osaka Prefectural University, Japan. He is now the representative (theory and computing) of Hirakata Ransu Factory (HRF).
Hiroshi Nakazawa obtained his DSci (statistical physics) at Kyoto University, Japan. As a professor at Takuma National College of Technology, Japan, he enjoyed teaching students applied mathematics. He is now the representative (theory and general affairs) of HRF.
Hiroshi Nakazawa obtained his DSci (statistical physics) at Kyoto University, Japan. As a professor at Takuma National College of Technology, Japan, he enjoyed teaching students applied mathematics. He is now the representative (theory and general affairs) of HRF.
Content
1. Basic Concepts and Tools 2. Group Structures 3. Designs of MC Generators 4. Lattice Structures 5. Regular Simplexes and Regular Lattices 6. Extended Second-Degree Tests 7. MC Generators with Excellent Statistics 8. MC Random Numbers on Spatial Lattices 9. Random Vector Fields and Random Walks 10. Two Addenda and Closing Comments