Eigen characters into least-square method
$begingroup$
I want to ask how to proove the $$widehat{z} $$
by using the eigen characters into least-square method?
Q:
$$y=Kz$$ where K is a nxn matrix and is a kernel with eigenfunctions
$$ lambda_m psi_m=Kpsi_m$$
and
$$intpsi_mpsi_n=delta_m,_n$$
that is
$$widehat{z}=sum_mlambda_m^{-1}y_mpsi_m $$
where
$$y_m=int y psi_m$$
I only could calculate that $$K^{-1}=lambda_m^{-1} $$
and why not just
$$z=K^{-1}y?$$
matrices eigenvalues-eigenvectors least-squares
asked Dec 15 '18 at 14:29
YuiYui
135
$endgroup$
add a comment |
$begingroup$
I want to ask how to proove the $$widehat{z} $$
by using the eigen characters into least-square method?
Q:
$$y=Kz$$ where K is a nxn matrix and is a kernel with eigenfunctions
$$ lambda_m psi_m=Kpsi_m$$
and
$$intpsi_mpsi_n=delta_m,_n$$
that is
$$widehat{z}=sum_mlambda_m^{-1}y_mpsi_m $$
where
$$y_m=int y psi_m$$
I only could calculate that $$K^{-1}=lambda_m^{-1} $$
and why not just
$$z=K^{-1}y?$$
matrices eigenvalues-eigenvectors least-squares
asked Dec 15 '18 at 14:29
YuiYui
135
$endgroup$
add a comment |
$begingroup$
I want to ask how to proove the $$widehat{z} $$
by using the eigen characters into least-square method?
Q:
$$y=Kz$$ where K is a nxn matrix and is a kernel with eigenfunctions
$$ lambda_m psi_m=Kpsi_m$$
and
$$intpsi_mpsi_n=delta_m,_n$$
that is
$$widehat{z}=sum_mlambda_m^{-1}y_mpsi_m $$
where
$$y_m=int y psi_m$$
I only could calculate that $$K^{-1}=lambda_m^{-1} $$
and why not just
$$z=K^{-1}y?$$
matrices eigenvalues-eigenvectors least-squares
asked Dec 15 '18 at 14:29
YuiYui
135
$endgroup$
I want to ask how to proove the $$widehat{z} $$
by using the eigen characters into least-square method?
Q:
$$y=Kz$$ where K is a nxn matrix and is a kernel with eigenfunctions
$$ lambda_m psi_m=Kpsi_m$$
and
$$intpsi_mpsi_n=delta_m,_n$$
that is
$$widehat{z}=sum_mlambda_m^{-1}y_mpsi_m $$
where
$$y_m=int y psi_m$$
I only could calculate that $$K^{-1}=lambda_m^{-1} $$
and why not just
$$z=K^{-1}y?$$
matrices eigenvalues-eigenvectors least-squares
matrices eigenvalues-eigenvectors least-squares
asked Dec 15 '18 at 14:29
YuiYui
135
asked Dec 15 '18 at 14:29
YuiYui
135
asked Dec 15 '18 at 14:29
YuiYui
135
asked Dec 15 '18 at 14:29
YuiYui
135
asked Dec 15 '18 at 14:29
YuiYui
135
135
add a comment |
add a comment |
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