How to solve system of nonlinear equations (A-x1)*x2=B?

A and x1 are 300*1 vectors, x2 is a 1*2000 vector, B is a 300*2000 sparse matrix.

(A-x1)*x2=B

we know A, B, then how can we calculate both vector x1 and x2?

Answer 1

[Torsten]

Choose x1_i (1<=i<=300) arbitrarily and x2_j = b_ij/(a_i-x1_i) (1<=j<=2000).

Best wishes

Torsten.

[Wanda Love]

Thanks Torsten, can I calculate x1 and x2 at the same time? actually, x1 is a noisy vector which I cannot anticipate how does it look like, and I am expecting to get it as well.

[Torsten]

As I already posted, there are infinitly many solutions for x1 and x2 that satisfy your above equations.

If you prescribe x1, then x2 is uniquely determined.

Best wishes

Torsten.