- #1
FrankST
- 24
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Dear All,
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
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