Algorithm 1.

Matrix-Free Computation of $\mathbf{M}\underset{\_}{u}$

procedure Computing $\underset{\_}{p}=\mathbf{M}\underset{\_}{u}$;

$\underset{\_}{p}=[]$ (initialization by null-vector)

for id = 1 to Nd do

$\underset{\_}{e}\leftarrow \tilde{\mathbf{E}}\left\{i_d\right\}$; $\underset{\_}{t}\leftarrow \tilde{\mathit{T}}\left\{i_d\right\}$; $\mathbf{N}\leftarrow \tilde{\mathbf{N}}\left\{i_d\right\}$

$\mathbf{R}\leftarrow t(\underset{\_}{e},:)$

$\mathbf{H}\leftarrow \underset{\_}{u}(\mathbf{R})$

$\mathbf{V}\leftarrow \mathbf{N}.\ast \mathbf{H};\underset{\_}{J}\leftarrow {\sum }_{t=1}^3\mathbf{V}(:,3)$

$\underset{\_}{I}=sparse\left(1,\underset{\_}{t},\underset{\_}{J},1,N_t\right)$

$\underset{\_}{p}\leftarrow {\left[{\underset{\_}{p}}^T,\frac{\left[I\left(2:N_t\right)0\right]-\left[0I\left(1:N_t-1\right)\right]}{2}\right]}^T$

end for

return $\underset{\_}{p}$

end procedure