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I have a linear system of equations such as Ax = b where A is a m-by-n matrix and m < n and A is a full rank matrix (rank(A) = m).

Since there are infinitely many solutions to this problem, I was looking for different methods to solve this problem. As I understood I can pose this problem as the following:

minimize 2-norm of x subject to: Ax = b

And I realized I can use pseudo inverse to find x . Here is my question:

1- Is the way I posed the problem correct or if there is an alternative way?

2- If A is a large and sparse matrix (like 30,000 by 200,000 matrix) is there a more efficient method to solve this problem (iterative methods) ?

3- If I want to impose additional constraints such that 0 <= x's <= 1 how can I do that ?

Thanks for your help,

Frank

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# Solving a large under-determined system of linear equations

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