The Best of the 20.th Century.pdf — Top 10 Algorithms
1946, Monte Carlo method; 1947, Simplex method; ...;
1962: Quicksort; ...
Computation
(since 1998) — Welcome to my webpages !
Prof. Victor M. Ponce (since 2000),
'Vlab',
San Diego State Univ., CA (USA)
What is this (below) ? 
ManyRandom.xlsx.
Are these random numbers "good" ?
Why 0.5 and 0.288675....pdf ?
Play a game: The Kruskal count card trick
RNG:
random number generation
mid-square technique.xls, by John von Neuman
Linear congruential.xls generator
Is simulation a panacea ? Yes, but beware... it may not be necessary:
Two Gaussian bars.xlsx .
If you insist: Sum of two Gaussians (!)
(Why is all this done in Fortran ?
Is it your fault ?)
(Shall I guess a digit that is in one of your notes ?)
Sometimes, the results are surprising:
Add some bars (trick ? yes, they are uniform).
So, uniforms are friendly ? Try
this (analytical).
(The integral is, of course, 1.)
Throwing dice.
The "other" use of Monte Carlo is to integrate (numerically),
namely for n ≥ 2.
How to simulate ?
Inversion method
for some common variables
Simulate a parabolic variable
(inverting a cubic !)
(See also acceptance-rejection,
Box-Muller, etc., as particular cases.)
Examples:
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(In Excel)
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| Estimating σ from sums (only) from unequal size samples (CISTI 2018, Spain) | |
Simulate (Gaussian) correlated variables:
2D, area (such as area of a paving slab); or
3D, bricks (volume, with algorithm)
Cholesky decomposition
