Higher-order splines all mostly look like Gaussians. I wonder how higher-order splines (from 3rd order onwards) and Gaussians differ. How can one differentiate them?


closed as unclear what you're asking by Peter K. Aug 26 '16 at 19:04

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  • $\begingroup$ They are actually different because 3rd order splines are only twice differentiable whereas Gaussians are infinitely differentiable. $\endgroup$ – Atul Ingle Aug 26 '16 at 16:56
  • $\begingroup$ By "differentiate" do you mean "take the derivative of them" or "distinguish between them" ? $\endgroup$ – Peter K. Aug 26 '16 at 19:04
  • $\begingroup$ Could add some details about the context you are asking this question in? $\endgroup$ – Laurent Duval Aug 28 '16 at 17:40
  • $\begingroup$ Exponential splines are new type of splines developed from one sided exponents, from this idea I had designed a new type splines from double sided exponents, In a recent conference one question was asked how my spline is different from standard Gaussians.. $\endgroup$ – Abhishek Sadasivan Jan 12 '17 at 17:51

If you talk about standard splines, piecewise polynomial, without tricks like orthogonalisation, they ought to have finite support. Not the case with Gaussians. As said by @Atul Ingle, derivability is another criterion, but might be more difficult to address on discrete data.


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