Random number generators by M-sequences with high-dimensional equidistribution property,and their dynamic creation M系列を用いた高次元均等分布性を持つ乱数の発生法とその動的生成
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Bibliographic Information
- Title
-
Random number generators by M-sequences with high-dimensional equidistribution property,and their dynamic creation
- Other Title
-
M系列を用いた高次元均等分布性を持つ乱数の発生法とその動的生成
- Author
-
松本, 眞
- Author(Another name)
-
マツモト, マコト
- University
-
東京大学
- Types of degree
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博士 (工学)
- Grant ID
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乙第14656号
- Degree year
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2000-03-16
Note and Description
博士論文
Table of Contents
- Contents / p2 (0003.jp2)
- 1 An Overview on Random Number Generation / p4 (0005.jp2)
- 1.1 Introduction / p4 (0005.jp2)
- 1.2 Necessity of good PRNG / p4 (0005.jp2)
- 1.3 Existing methods: integers versus finite fields / p5 (0006.jp2)
- 1.4 Basic results on linear recurrence over a field / p7 (0008.jp2)
- 1.5 Theoretical analysis: k-distribution properties / p10 (0011.jp2)
- 1.6 Various statistical tests / p11 (0012.jp2)
- 1.7 Historical comments / p12 (0013.jp2)
- 2 Mersenne Twister / p13 (0014.jp2)
- 2.1 MT Algorithm / p13 (0014.jp2)
- 2.2 The performance of MT / p18 (0019.jp2)
- 2.3 Key ideas in MT / p21 (0022.jp2)
- 2.4 A method to find the period parameters / p24 (0025.jp2)
- 2.5 A method to find tempering parameters / p29 (0030.jp2)
- 3 Dynamic Creation of PRNG / p33 (0034.jp2)
- 3.1 The necessity of parallel PRNG / p33 (0034.jp2)
- 3.2 Dynamic Creation / p33 (0034.jp2)
- 3.3 Experiments on Dynamic Creation / p35 (0036.jp2)
- 3.4 The arithmetics on F₂ realizes DC / p37 (0038.jp2)
- 4 Appendix / p39 (0040.jp2)
- 4.1 Appendix A. Explicit form of the transition matrix / p39 (0040.jp2)
- 4.2 Appendix B. Obstructions to optimal distribution / p39 (0040.jp2)
- 4.3 Appendix C. C-code / p43 (0044.jp2)
