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CSC201 Solution of Simultaneous Algebraic Equations Using Lower-Upper Decomposition Method

Solved assignment explaining LU decomposition for solving simultaneous algebraic equations.

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    CSC201 Solution of Simultaneous Algebraic Equations Using Lower - Upper Decomposition Method CSC201 Project # 3 Summer15 Print Name: _____________________________________________________ Academic Honesty Policy : Students at the college are expected to be honest and forthright in their academic endeavors. To falsify the results of one’s research, to steal the words or ideas of another, to cheat on an examination, or to allow another to commit an act of academic dis honesty corrupts the essential process by which knowledge is advanced. It is the official policy of the Northern Virginia Community College that all acts or attempted acts of alleged academic dishonesty be reported to the Dean of S tudents Office. By signing below, I acknowledge that I have read the above and that I have neither given nor received assistance on this examination. Sign Name: _______________________________________________________ 3. Solution of Simultaneous Algebraic Equations ***: In algebra, we often have to solve simultaneous differential equations. If the equations are linear and independent, there is a unique solution when the number of equations equals the number of variables. If there are only two variables and two equations, it’s easy, but as the number of equations and unknowns increases, the problem becomes more difficult. Imagine, for example trying to solve 100 equations in 100 unk nowns. That's an unthinkably difficult manual exercise, but a good computer program can do it in less than a second. Suppose you want the solution to this pair of equations: 2 * x + y = 1 4 * y = 12 In the first equation, the coefficient of x is 2 and the coefficient of y is 1 . In the second equation, the coefficient of x is 0, and the coefficient of y is 4. The right - side values are 1 and 12, respectively. It's easy to solve this pair of equations by hand. The second equation says y = 12/4 = 3, and substituting this back into the first equation gives x = (1 - 3)/2 = - 1. The program you'll write will solve this problem like this: Sample session : Number of Equations & Unknowns: 2 Enter equation 0's coefficients separated by spaces:

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    2 1 Enter right - side value: 1 Enter equation 1's coefficients separated by spaces: 0 4 Enter right - side value: 12 Equations 2.0 1.0 1.0 0.0 4.0 12.0 Solution - 1.0 3.0 Verification 1.0 1.0 12.0 12.0 The numbers under “Verification” show a comparison between the original right - side values (first column) with what the computer gets when it substitutes it’s solution back into the original equations (second column). It’s not worthwhile writing a computer program to s olve a simple problem like this, but it would be worthwhile if you had to solve 10 equations with 10 unknowns, and suppose you had 200 equations with 200 unknowns? This project’s program will be able to solve even a problem of that size, with no sweat. Often it’s useful to put a hard - coded default example into your code, to keep you from having to re - enter everything when debugging. You could use an unreasonable input like zero to generate a test case: Another sample session : Number of Equations & Unknowns: 0 Equations - 6.0 33.0 16.0 - 36.0 - 7.0 34.0 - 8.0 43.0 - 25.0 22.0 9.0 - 46.0 Solution 1.310701412279147 0.7545943390651776 - 3.3148377947172487 Verification - 36.0 - 36.0

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