Over-determined system

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parham kianian 2019-11-13

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关闭： John D'Errico 2019-11-13

Dear Friends,

I want to solve an over-determined system in the form of max(abs(A*x)) = B;

size(A) = n by m

size(x) = m by 1

size(B) = n by 1

n > m

NOTE: A is a cell array which each Aij is vector of length L

Is there any built in function in MATLAB that solves such systems?

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parham kianian 2019-11-13

Dear John,

I need to solve a system of over-determined equations as follow:

max(abs(A11*x1 + A12*x2 + ... + A1m*xm)) = B1

max(abs(A21*x1 + A22*x2 + ... + A2m*xm)) = B2

max(abs(An1*x1 + An2*x2 + ... + Anm*xm)) = Bn

and in matrix form: max(abs(A*x)) = B.

x is the vector of unkonws with m number of arrays. B is the vector of knowns with n number of arrays and finally A is a n by m matrix. But the issue is that each array of matrix A is a vector. This is why I used the functions of max and abs in the system of equations. Note that this is an over-determined system, that is, the number of equations (n) is greater than the number of unknowns (m).

Is there any MATLAB fuction to solve such system of equations?

I hope this explanation clarifies the issue.

John D'Errico 2019-11-13

Now I remember. You asked exactly this question before, but did not get an answer, so you are asking it again. Only this time, you asked it in a hidden way to make it look like a different problem. Only in your comment do you disclose it is identical.

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