Minimize difference between vectors by varying scalar

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alberto tonizzo
alberto tonizzo 2022-5-18
评论： alberto tonizzo 2022-5-22
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.
  1 个评论
Torsten
Torsten 2022-5-18
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.

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Torsten
Torsten 2022-5-18
编辑：Torsten 2022-5-18
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.

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