Algorithm 4.

Low-memory Laplace transformed “ijkabc” algorithm.

for q = 1, nq
Perform transformation and assembly steps of Eqs. (27)–(30), but not Eq. (31)
${\mathcal{I}}_{ā\overline{b},\overline{c}}^{\overline{K}}={\mathcal{J}}_{\overline{a}\overline{c}}^P{\mathcal{J}}_{\overline{b}\overline{K}}^P$, only for K = 1
for J = 1, no
if (new block begins) ${\mathcal{I}}_{ā\overline{b},\overline{c}}^{\overline{L}}={\mathcal{J}}_{\overline{a}\overline{c}}^P{\mathcal{J}}_{\overline{b}\overline{L}}^P$ for $J\le L<J+n_{\mathrm{B}}$
if ($J+n_{\mathrm{B}}-1<n_{\mathrm{o}}$) $A_{\overline{b}\overline{c},P}^{\overline{J}\overline{K}}=T_{\overline{b},\tilde{d}}^{\overline{J}\overline{K}}{\left({\mathcal{J}}_{\overline{c},\overline{d}}^P\right)}^{†}+{\mathcal{J}}_{\overline{b},\overline{d}}^P{\left(T_{\overline{c},\tilde{d}}^{\overline{K}\overline{J}}\right)}^{†}$
for $I\ge J$
if ($I<J+n_{\mathrm{B}}$) $v_{cab}\leftarrow T_{\overline{c},\tilde{d}}^{\overline{K}\overline{J}}{\mathcal{I}}_{\overline{d},ā\overline{b}}^{\overline{I}}+{\mathcal{I}}_{\overline{c}ā,\overline{d}}^{\overline{I}}{\left(T_{\overline{b},\tilde{d}}^{\overline{J}\overline{K}}\right)}^{†}$
else $w_{abc}\leftarrow {\mathcal{J}}_{ā\overline{I}}^P{A}_{\overline{b}\overline{c},P}^{\overline{J}\overline{K}}$
The remaining 10 terms, which do not include the above two terms [c.f., Eq. (B1)] are
evaluated as shown in Algorithm 2
end for
end for
end for