Minimize difference between vectors by varying scalar

Hello,

I'm trying to use fminsearch to find the scalar (a) that minimizes the difference between 2 vectors of dimension N, i.e. diff = abs(x - a*x_model).

The difference (diff) is a vector of dimensions 1xN and fminsearch outputs also a vector of dimensions 1xN, but I would like to just have a scalar value for a.

Also, should diff be normalized by the mean of x?

I hope my explanation is clear, thank you in advance.

[Torsten]

You cannot minimize a vector (in your case diff = abs(x-a*x_model)). You can minimize the norm of a vector.

For diff = x-a*x_model, you must decide which norm to take.

Answer 1

[Torsten]

a = x_model\x

minimizes

norm(a*x_model - x)

If you want to minimize the difference in another norm (e.g. max(abs(a*x_model-x)) or sum(abs(a*x_model-x))), the solution will be different.

[alberto tonizzo]

Thank you!