Algorithm 3 Multilinear interpolation with Boundary (MLBD) method

$$\begin{array}{cc}\hfill & \mathrm{Input}:\mathsf{Pre}\text{-computed values}{F}^{-1}({\tau }_l,{\Delta }_m,{\Delta }_q)\mathsf{on}\mathsf{a}\mathsf{fixed}\mathsf{grid}({\tau }_l,{\Delta }_m,{\Delta }_q)\in \mathcal{G}\hfill \\ \hfill & \mathsf{based}\mathsf{on}\mathsf{the}\mathsf{type}\mathsf{of}\mathsf{variables}j\mathsf{and}k.\hfill \\ \hfill & \text{1:2}.\text{Same}\text{as}\text{Algorithm}1.\hfill \\ \hfill & 3.\mathsf{if}\mid {\widehat{\tau }}_{jk}\mid \le 0.9\text{ABD}\text{in}(9),\text{apply ML Algorithm}2.\hfill \\ \hfill & \mathsf{if}\mid {\widehat{\tau }}_{jk}\mid >0.9\text{ABD},\text{apply ORG Algorithm}1.\hfill \end{array}$$