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You don't need to use O(n^3) Gaussian elimination to find natural cubic splines: you can write the system of equations as a tridiagonal matrix, which can be sol
by creata 3y ago
You don't need to use O(n^3) Gaussian elimination to find natural cubic splines: you can write the system of equations as a tridiagonal matrix, which can be solved in linear time.
https://splines.readthedocs.io/en/latest/euclidean/natural-uniform.html#Solving-the-System-of-Equations https://splines.readthedocs.io/en/latest/euclidean/natural-u...
- dahart 3y agoYou don’t need to solve a system of equations at all, and it’s unusual to do so unless you have very specific requirements, right? All of the reasons the article used to justify going that direction can be met (more or less, depending on more nuance than the article used) with existing spline types. Plus you can trade some of the overshoot properties of the article’s solution for just a little bit of extra curvature, with a Catmull-Rom spline for example, which might be preferable for many people for multiple reasons.
- jacobolus 3y agoHere's a write-up I made a couple years ago which I think does a bit better describing the math in question: https://observablehq.com/@jrus/cubic-spline https://observablehq.com/@jrus/cubic-spline