But the type of barycentric interpolation formula that leads to Inf/Inf at an interpolation point isn't one of those exceptions - it's an example which shows why the rule should be borne in mind.
When the input is very close to one of the interpolation points, the calculation becomes ill-conditioned, unsurprisingly as two values are diverging towards Inf, so the result can become incorrect as the input approaches the interpolation point, until it becomes Inf/Inf = Nan at some even closer, but non-zero, distance. Before reaching Nan it can also have an interval where the result is +/-Inf.
It depends on the interpolation points. But under some circumstances, it is necessary to recognise when the input is close to an interpolation point, and adjust the formula appropriately.
But the type of barycentric interpolation formula that leads to Inf/Inf at an interpolation point isn't one of those exceptions - it's an example which shows why the rule should be borne in mind.
When the input is very close to one of the interpolation points, the calculation becomes ill-conditioned, unsurprisingly as two values are diverging towards Inf, so the result can become incorrect as the input approaches the interpolation point, until it becomes Inf/Inf = Nan at some even closer, but non-zero, distance. Before reaching Nan it can also have an interval where the result is +/-Inf.
It depends on the interpolation points. But under some circumstances, it is necessary to recognise when the input is close to an interpolation point, and adjust the formula appropriately.