# Solving 2000 Linear equations with apporximation

Budget $250-750 USD

I am looking for approximately 2000 unknown prices of (health related) activities. The total price of the same amount of products which are build up by the activities are known. This makes the problem a simple linear solving problem where one should solve the matrix equation Ax=b. (A is amount of activities (matrix), x are the unknown prices of the activities (vector) and b is the total price of the product).

It should be simple however Mathematica seems to have trouble with the amount of equations, or the scale of the matrix (2000x2000).

Furthermore, the system cannot be solved uniquely because the prices and amounts are not that accurate. Therefore I need to have an approximation of the prices for each activity, and not the unique solution.

Last but not least, I need a program that ensures that the final outcome of prices are not negative. If one would use a normal Linear Solver (in Mathematica for instance), you sometimes get negative numbers for x_i, which is not possible as I am looking for prices.

A want a program that :

1. Reads a matrix and vector as input

2. Approximates the outcome x with loops, where I can set the ranges in which my prices should lie.

3. As output a vector x which corresponds to a specific activity and that has a price between a predefined range.

A C++ program would do, if you can help install the necessary software on my Windows pc.

Thank you in advance.

## 19 freelancers are bidding on average $335 for this job

Dear sir, I am strong in C++ programming especially in algorithm implementation. I am familiar with linear programming and have implemented simplex. I have also implemented matrix calculation and equation solution. More

I had a project concerning (implementation and comparison) different methods to solve systems of equations. I can do this.

Hi, sounds like an interesting project. However my solution will be coded in C#. If interested in my bid please contact me for further discussion. Regards.

I'm a PhD Candidate who has worked extensively in this area. The problem should be relatively easy to solve. Please see your PMB for some ideas

I've taken another look at the problem and maybe latest program does a better job. Will forward today's solution. But just noticed there was another small problem. Still, it gives some confidence it will eventually get More

I am postgraduate student in the department of Applied Mathematics and Informatics majoring Differential Equations. I can do this job.