Solving Separable Least Square Problem - Isy

[isolde_isy]

Hi I have to solve the following LSQ problem:
min(||Aax-b||2)

where
A is a known matrix,
b is a know vector
x is an unknows vector
a is an unknown scalar

I can solve directly via pseudo inverse
ax=inv(A'A)A'b
but how can I isolate a from x?

Could Separable least square a scheme to follow...
Thnaks in advance
Isy

 

[mathman]

Unless you have some particularly property (for example the magnitude of x = 1), you can't "separate" a from x. Your solution is a vector.

 

[isolde_isy]

So it can be reformulate the problem in lsq constrained
min(||Aax-b||2)
subject to ||x||=1

Right?
Thanks Isy

 

[mathman]

So it can be reformulate the problem in lsq constrained
min(||Aax-b||2)
subject to ||x||=1

Right?
Thanks Isy

Yes - but note that there would (for real vector spaces) be two possibilities, since a and -a, associated with x and -x would satisfy.