- #1
divB
- 87
- 0
Hi,
I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y the measurements.
Now WEIGHTED least squares allows to weight the MEASUREMENTS if, for example, some measurements are more important or contain a lower variance.
However, I am looking for a solution of putting weights on the coefficient vector. Pictorially speaking, some values in my coefficient vector c are more important than others and I would like emphasize some more than others using my limited set of N measurements.
Just adding a diagonal weighting matrix w as follows does not work:
[tex]
\min_c \| y - Awc \|_2
[/tex]
I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y the measurements.
Now WEIGHTED least squares allows to weight the MEASUREMENTS if, for example, some measurements are more important or contain a lower variance.
However, I am looking for a solution of putting weights on the coefficient vector. Pictorially speaking, some values in my coefficient vector c are more important than others and I would like emphasize some more than others using my limited set of N measurements.
Just adding a diagonal weighting matrix w as follows does not work:
[tex]
\min_c \| y - Awc \|_2
[/tex]