Nikratio
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Hello,
I need to invert a non-square matrix A under the constraint that the absolute value of each component of the solution is less than some maximum. In other words, I want \vec{b} such that A . \vec b = \vec c and |b_i| < \alpha.
Are there any established methods for doing this?
My idea is to start with the pseudoinverse to compute the unconstrained solution, and to then add components \vec v_i from the null space of A to satisfy the constraint. If this doesn't help, I wanted to consecutively add more basis vectors from the singular value decomposition of A, starting with the basis corresponding to the smallest singular value.
However, I don't see how to pick the coefficients of the \vec v_i in such a way that the final solution is optimal in the sense that there is no other solution that satiesfies the constraints but has a smaller ||A.\vec b - \vec c||.
Anyone able to help? Pointers to appropriate literature would be appreciated as well, I am not quite sure what keywords I should be looking for.
I need to invert a non-square matrix A under the constraint that the absolute value of each component of the solution is less than some maximum. In other words, I want \vec{b} such that A . \vec b = \vec c and |b_i| < \alpha.
Are there any established methods for doing this?
My idea is to start with the pseudoinverse to compute the unconstrained solution, and to then add components \vec v_i from the null space of A to satisfy the constraint. If this doesn't help, I wanted to consecutively add more basis vectors from the singular value decomposition of A, starting with the basis corresponding to the smallest singular value.
However, I don't see how to pick the coefficients of the \vec v_i in such a way that the final solution is optimal in the sense that there is no other solution that satiesfies the constraints but has a smaller ||A.\vec b - \vec c||.
Anyone able to help? Pointers to appropriate literature would be appreciated as well, I am not quite sure what keywords I should be looking for.