alt Hacker NewsCurious, is there some alternative that would give you both higher order continuity and numerical stability? Or are they fundamentally at odds?
Curious, is there some alternative that would give you both higher order continuity and numerical stability? Or are they fundamentally at odds?
IMO, higher order continuity is a red herring. You can make something approximately high order continuous (say, to 10+ digits, or whatever you like) piecewise much more easily than enforcing mathematically exact high order continuity. Once you think of continuity as something to achieve approximately, standard methods from classical approximation theory suffice.