Matlab Math 随机数 Cleve morler著 陈文斌(wbchen@fudan.edu.cn) 复旦大学2002
Matlab Math Cleve Morler著 陈文斌（wbchen@fudan.edu.cn) 复旦大学2002 随机数
Pseudorandom number 0.95012928514718 MATLAB format long, rand pseudorandom number: 1951, D H Lehmer, Berkeley A random sequence is a vague notion.. in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians
Pseudorandom Number format long; rand 0.95012928514718 pseudorandom number: A random sequence is a vague notion …. in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians… 1951, D.H. Lehmer, Berkeley
An Extended Theory of Lucas Functions By D. H Lehmer Here is a page from Int roduction Lehmer's famous It is ore than half a century since the appearance of Lucas meso 7h;dF“ct。:r; QW.s SimpL票6nt dissertation on the functions named after 194239,289-821·(1878) recurring series of the second order is a study of the two the french sy血 metric functiong (141)7n(a-,”)/(e mathematician edouard of the roots of the quadratic equation; ',a"+, e-b) (1,2) x2. Lucas(1842-1891).It with constant relatively prime integral coefficients. The results of his investigations are partly algebraic and partly number. subsequently appeared thoorotio, The algebraic rosulta are unchanged if the restrictions in Annals of which he puts on P and o are renoved by letting these const ants be Mathematics and as a any real or complex numbers, The fundamental character of U and Pa is well portrayed in the numerous developments and rel ations monograph published that involve as special cages the trigonometric, hyperbolic, cyclo- tomic and logarit hnic funotions.. The algebraic theory is based on in Hamburg by lutcke the difference equations Wulff both in 1930 (1.2) Un.2 -PUn, 1-9Jn and n 2.PV.1-gFn From the algebraic theory Lucas builds up the number- t heoretic properties, of U and 7n by changing his equations to congruences In this part of the development it becomes necessary to consider the
Here is a page from Lehmer's famous dissertation on the functions named after the French mathematician Edouard Lucas (1842-1891). It subsequently appeared in Annals of Mathematics and as a monograph published in Hamburg by Lutcke & Wulff, both in 1930
Lehmer's algorithm Multiplicative congruential algorithm: HE& a, c,m 种子:x0 ki=axk +c mod m 例如:a=13,c=0,m=31,x0=1,输出 11314271061622729538 周期:m-1。可以通过除以m来得到[0,1的一致分布的数 0.03230.4194045160.87100.32260.19350.5161 最小值:1/31,最大值:30/31
Lehmer's Algorithm Multiplicative congruential algorithm: 整数 a,c,m 种子： 0 x xk 1 axk c mod m 1 13 14 27 10 6 16 22 7 29 5 3 8 例如：a=13, c=0, m=31, x0=1，输出： 周期：m－1。可以通过除以m来得到[0,1]的一致分布的数 0.0323 0.4194 0.4516 0.8710 0.3226 0.1935 0.5161… 最小值：1/31,最大值：30/31