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This isn't a bad mnemonic but it's not true in general - interpolation just means estimating missing data and you don't need to use polynomials eg gaussian inte
by mathisfun123 3y ago
This isn't a bad mnemonic but it's not true in general - interpolation just means estimating missing data and you don't need to use polynomials eg gaussian interpolation is a thing. Polynomials are the most common simply because they're the easiest/fastest to fit.
- xeonmc 3y agoI'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