Midsquare method- simulation system
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The document introduces the mid-square random number generation method, invented by John von Neumann, which involves squaring a seed number and extracting digits to produce pseudorandom numbers, though it is not reliable due to its short period. It outlines the method, provides an example of generating random numbers, discusses its limitations, and highlights various applications of random numbers in fields like simulation, sampling, numerical analysis, and decision-making. The document concludes by noting the historical and recreational significance of randomness, linking it to the Monte Carlo method.
Midsquare method- simulation system
- 1. Welcome
- 2. Topic Name : Mid-Square Random Number Generation Presented By Md: Arman Hossain
- 3. OUTLINE Introduction Mid-square Method Example of Mid-square Departures of Mid-square Method Applications of Random Numbers References
- 4. INTRODUCTION Mid-square method was invented by John von Neumann, and was described at a conference in 1949. In mathematics, the mid-square method is a method of generating pseudorandom numbers. In practice it is not a good method since its period is usually very short.
- 5. Mid-square Method 1. Starting with n digit number 2. Squaring it 3. For 8 digit : Remove two lower and higher order digit 4. For 7 digit : Remove one lower and two higher order digit 5. Taking n digits in the middle as the next number 6. Repeat from number no. 2.
- 6. Example of Mid-square For an example, we are using 4 digit which is called seed number, we are showing generate 5 random number here, 5673 1. (5673)2 = 32 1829 29 = 1829 2. (1829)2 = 3 3452 41 = 3452 3. (3452)2 = 11916304 = 9163 4. (9163)2 = 83960569 = 9605 5. (9605)2 = 92256025 = 2560 Remove two higher order digit Remove two lower order digit Next seed number Square seed number Remove one higher order digit Remove two lower order digit
- 7. Departures of Mid-square Method Converge on a constant : 2500 (2500)2 = 6 2500 00 = 2500 This will repeated. 2504 (2504)2 = 6 2700 16 = 2700 (2700)2 = 7 2900 00 = 2900 (2900)2 = 8 4100 00 = 4100 . . (2100)2 = 4 4100 00 = 4100 This will repeated also. There more constant number like this. seed seed
- 8. Applications of Random Numbers Simulation : when a computer is being used to simulate natural phenomena, random numbers are required to make things realistic. Simulation covers many fields, from the study of nuclear physics to operations research. Sampling : It is often impractical to examine all possible cases, but a random sample will provide insight into what constitutes “typical behavior”. Numerical analysis : Ingenious techniques for solving complicated numerical problems have been devised using random numbers. Computer programming: Random values make a good source of data for testing the effectiveness of computer algorithm. Decision making : There are reports that many executives make their decisions by flipping a coin or by throwing darts, etc. It is also rumored that some college professors prepare their grades on such a basis. Sometimes it is important to make a completely "unbiased decision; this ability is occasionally useful in computer algorithms, for example in situations where a fixed decision made each time would cause the algorithm to run more slowly. Randomness is also an essential part of optimal strategies in the theory of games. Recreation : Rolling dice, shuffling decks of cards, spinning roulette wheels, etc., are fascinating pastimes for just about everybody. These traditional uses of random numbers have suggested the name "Monte Carlo method," a general term used to describe any algorithm that employs random numbers.
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