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Over-determined system of equations

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parham kianian
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
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?
parham kianian
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.

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