algorithm - Findig a solution for a linear equation system which has more variable then equtions -


This problem is divided into two halves, the second option is optional.

Part 1

I have 3 linear acuctions with variables of N, where N is usually larger.

  • x1 * a + x2 * b + x3 * c + x4 * d [....] xn * p = b1
  • y1 * a + y2 * B + y3 * c + y4 * d [....] yN * p = b2
  • z1 * a + z2 * b + z3 * c + z4 * d [....] zn * P = b3

(a, b, c, d, [...], p), the other are static.

The standard will not work in gaussian mode because the matrix is ​​longer then lengthy. Of course I can use it to eliminate 2 variables. Do you know an algorithm for finding a solution? (I only need one.) The solution coefficient is more 0s but it is not necessary.

part 2

Coefficient must be non-negative in the solution.

Requirements: The algorithm must be adequately adequate to run real time. (1800 per second on an average PC) so the test and error method is not one. The algorithm will be applied to C #, but if you want to write the code, do not hesitate to use the pseudo language.

Set the additional variable to zero We now have the matrix equation

Ax = B, where 

  x1x2x3

a = y1 y2 y3 z1 z2 z3

b = (b1, b 2, B3), now inverted as a column vector. The solution is;

X = A -1 .x

Finally enter the Ctrl key into the matrix formula in Excel


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