simultaneous equations
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I am looking to solve two simultaneous equations for two unknown matrices of the form:
[Y1]=a1+a2[X1]+a3[X2]+a4[X1]^2+a5[X2]^2+a6[X1][X2]
[Y2]=b1+b2[X1]+b3[X2]+b4[X1]^2+b5[X2]^2+b6[X1][X2]
Where [Y1] & [Y2] are known matrices, [X1] & [X2] are unknown matrices and a1 to a6 & b1 to b6 are scalar coefficients.
Could anyone suggest how I might go about doing this in Matlab?
Cheers,
Joe
1 个评论
Chaowei Chen
2011-8-22
My quick bet is to vectorize [Y1], [Y2], [X1], [X2].
One question I am not sure about is [Xk]^2 and [X1][X2].
Are they regular matrix multiplication or element-by-element multiplication?
But either way, vectorization still works if I understand your question correctly. For example, your [Y1] is a 2 by 2 matrix. You can vectorize
[Y1]=a1+a2[X1]+a3[X2]+a4[X1]^2+a5[X2]^2+a6[X1][X2]
into 4 equations.
Just write out and compare each element on left and right side of the equations.
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