Algorithm A.4.

function BandlimitingWeights (Λ^(X), Λ^(Y), $\ell$) = w^{(X, Y)}

Compute the joint bandlimiting weights for two graphs.

Input:		Normalized Laplacian eigenvalues	$\mathrm{\Lambda }=\left\{{\mathrm{\Lambda }}^{(X)},{\mathrm{\Lambda }}^{(Y)}:{\mathrm{\Lambda }}^{(Z)}={\left\{{\lambda }_j^{(Z)}\right\}}_{j=2}^{\#|Z|}\right\}$
		Alignment band count	$\ell$
Output:		Pairwise frequency weights	$w^{(X,Y)}:{\mathrm{\Lambda }}^{(X)}\times {\mathrm{\Lambda }}^{(Y)}\mapsto [0,1]$
1:	$f\leftarrow f:\lambda ,\ell ,\xi \mapsto I(\xi -1\le \lambda \ell \le \xi +1)\sin \left(\frac{\pi }{2}{\cos }^2\left(\frac{\pi }{Y}(\ell \lambda -\xi )\right)\right)$			▷ Itersine wavele 4.1
2:	for i = 2, N2 do
3:	for j = 2, N2 do
4:	$w_{ij}(X,Y)\leftarrow 0$
5:	for ξ = 1, $\ell$ do
6:	$w_{ij}{}^{(X,Y)}\leftarrow w_{ij}{}^{(X,Y)}+f\left({\lambda }_i{}^{(X)},\ell ,\xi \right)f\left({\lambda }_j{}^{(Y)},\ell ,\xi \right)$
7:	end for
8:	end for
9:	end for
10:	return w(X, Y)