Least Squares

Suppose we would like to approximate the vector $ {\bf x}$ as a linear combination of the columns of some matrix $ {\bf H}$, or

$\displaystyle {\bf x}\simeq {\bf H} \; {\bf a},
$

where $ {\bf a}$ is a vector of coefficients. To find the least-squares approximation, we let

$\displaystyle {\bf a} = ({\bf H}^\prime {\bf H})^{-1} {\bf H}^\prime {\bf x}.$ (16.12)



Baggenstoss 2017-05-19