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

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Wanda Love
Wanda Love 2015-6-8
评论： Torsten 2015-6-8
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?

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回答（1 个）

Torsten
Torsten 2015-6-8
Choose x1_i (1<=i<=300) arbitrarily and x2_j = b_ij/(a_i-x1_i) (1<=j<=2000).
Best wishes
Torsten.
  2 个评论
Wanda Love
Wanda Love 2015-6-8
编辑：Wanda Love 2015-6-8
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
Torsten 2015-6-8
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.

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