This method uses linear interpolation of the survival fraction to build a mortality curve. Given a set of survival fractions \(\sfrac_i\) at ages \(x_i\) for \(i=0,\ldots,n-1\) the value at age \(x\in[x_i,x_{i+1})\) is \begin{equation} \sfrac(x) = \frac{x_{i+1}-x}{x_{i+1}-x_i}\sfrac_i + \frac{x-x_i}{x_{i+1}-x_i} \sfrac_{i+1} \end{equation} It follows that person-years lived across the age interval \([x_i,x_{i+1})\) is \begin{equation} L_i := \int_{x_i}^{x_{i+1}} \sfrac(a) da = \frac{1}{2}(x_{i+1}-x_i) (\sfrac_i + \sfrac_{i+1}) \end{equation} which is the common linear rule-of-thumb used to convert death rates to death probabilities. Notice that since the slope of the survival fraction is constant between nodes it follows from the definition for force \begin{equation} \label{eqn:force} \force(x)=-\frac{1}{\sfrac} \frac{d\sfrac}{dx} \end{equation} that the force is always increasing between nodes and will be discountinuous across nodes. Beyond the last finite age the buildmethod assumes a constant force \begin{equation} \sfrac(x) = \sfrac_{n-1} e^{-\oforce(x-x_{n-1})} \end{equation} where \(\oforce\) is the force in the open interval which is inferred from life expectancy at \(x_{n-1}\) if this is specified otherwise it is calculated using Equation\(~\ref{eqn:force}\).