Set up system of linear equations and solve

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i need to set up a system of linear equations and solve it. The calculations are based on a graph and are always of the same format. I need ideas how to solve my problem efficiently...

At first I create all necessary equations. Here is an example:

q = 4,9 + r
r = 2,3 + 0,03q + 0,11d + 0,85(1 + r)
d = 15,3 + 0,02q + 0,74r

This step is already done. My program creates this formulas. My problem is now, what is the most efficient way to calculate the values? I need to prepare the equations to be able to use them in a matrix solver. Hence, i have to eliminate the brackets and combine the values...

I thought of combining multiple java libraries to reach the goal. At first I wanted to use a simplifier to simplify all equations and finally a matrix solver to calculate the values. Here are my thoughts:

Step 1: Eliminate brackets if necessary)

q = 4,9 + r
r = 2,3 + 0,03q + 0,11d + 0,85 + 0.85r
d = 15,3 + 0,02q + 0,74r

Step 2: Combine values)

q = 4,9 + r
r = 3,15 + 0,03q + 0,11d + 0.85r
d = 15,3 + 0,02q + 0,74r

Step 3: Prepare matrix)

-4,9 = -q + r
-3,15 = -r + 0,03q + 0,11d + 0,85r
-15,3 = -d + 0,02q + 0,74r

Step 3.2: Combine values)

-4,9 = -q + r
-3,15 = -0,15r + 0,03q + 0,11d
-15,3 = -d + 0,02q + 0,74r

Step 3.3: Sort values)

-4,9 = -q + r
-3,15 = 0,03q - 0,15r + 0,11d
-15,3 = 0,02q + 0,74r -d

Step 3.4: Matrix structure)

-4,9 = -1 1 0
-3,15 = 0,03 -0,15 0,11
-15,3 = 0,02 0,74 -1

And now I can use a matrix solver like jama. There are several steps that have to be performed. But whats the most efficient way without reinventing the wheel?

Thanks in advance.

asked 2 mins ago

Ioannis K.

236

Set up system of linear equations and solve