nonlinear equation with matrix inverse

Hi guys,

Is there a Matlab function that can give me the solution of the following nonlinear equation:

(A+b*X)^-1=C+d*X,

where A and C are invertible Hermitian matrices, and b>0 and d>0 are scalars, "*" denotes product.

Thanks for your attention:)

Answer 1

[Matt J]

The equation can be reorganized as

 (C+d*X)*(A+b*X)-eye(N)=0

or

 (A+b*X)*(C+d*X)-eye(N)=0

This equation will not in general have a unique solution. It can also have no solutions. When X is 1x1, for example, it reduces to a quadratic equation.

However, you can try using FSOLVE to find one of the solutions.