3 ms·
I've edited my comment to remove the mention of interpolation, since it was only tertiary to the point I was making and, as you said, that description sacrifice
by xeonmc 3y ago
I've edited my comment to remove the mention of interpolation, since it was only tertiary to the point I was making and, as you said, that description sacrificed precision for brevity.
Also the use of polynomial isn't exactly just due to being "easier to fit", rather it's that it's a fundamental primitive of the derivative operator, it being easier to fit is more like a "perk" that arises. Kinda like saying that "we use integers because it's easier to represent with bits" -- not wrong, just that the cause and the reward is kinda backwards.
- mathisfun123 3y ago> rather it's that it's a fundamental primitive of the derivative operator People run away with their math woo... You're just talking about an eigenspace of a linear operator. It's true polynomials are closed under d but they're not special - sinusoids are the most obvious other example. There are countless other examples as soon you start building slightly more complicated differential operators.
- bigyikes 3y agoCan someone help me understand this comment thread? It seems really interesting but it is over my head. I can understand simple calculus and linear algebra.
- selimthegrim 3y agoClosed under D just means polynomial is the derivative of a polynomial etc. just like sinusoid of sinusoid and exponential of exponential