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# Over-determined system of equations

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parham kianian on 24 Oct 2019
Closed: MATLAB Answer Bot on 20 Aug 2021
Dear friends,
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
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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?
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parham kianian on 24 Oct 2019
Dear Fabio
consider first equation:
A11*x1 + A12*x2 + ... + A1m*xm is a vector. then the abs(A11*x1 + A12*x2 + ... + A1m*xm) is also a vector. finally the max(abs(A11*x1 + A12*x2 + ... + A1m*xm)) is scalar like B1. So the problem is well explained.
max(abs(A*x)) is not a vector. It is n number of vectors which max(abs(A*x)) becomes a vector with same size as B.
Note that each Aij is a vector. That is, arrays of matrix A are vectors not scalars.