Over-determined system of equations

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?

[Fabio Freschi]

A*x is a vector

abs(A*x) is a vector

max(abs(A*x)) is a scalar

while B looks like a vector. I think that your problem is not well explained.

[parham kianian]

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.