Notes on Lagrange Interpolating Polynomials • Hacker News Board

Re: Notes on Lagrange Interpolating Polynomials

#11

Post by looneysquash » Mon, Mar 02, 2026, 10:33 PM UTC

Maybe there's a gap in my knowledge of notation, but I was confused by:

> Let’s define the Lagrange basis functions

It looks like you defined `l_i(x)` as a piecewise function or a step function.

But then you show with it's actual definition later in that section. (That's what that section is building to and explaining.)

Re: Notes on Lagrange Interpolating Polynomials

#12

Post by drivebyhooting » Mon, Mar 02, 2026, 10:34 PM UTC

If we already have access the machinery of the fundamental theorem of algebra then the invertibility of the Vandermonde Matrix follows as a corollary.

Re: Notes on Lagrange Interpolating Polynomials

#13

Post by eliben » Mon, Mar 02, 2026, 11:53 PM UTC

looneysquash wrote: post #11

Maybe there's a gap in my knowledge of notation, but I was confused by: > Let’s define the Lagrange basis functions It looks like you defined `l_i(x)` as a piecewise function or a step function. But then you show with it's actual definition later in that section. (That's what that section is building to and explaining.)

Thank you for the feedback. The idea was to first define what we want the basis functions to be (a pretty abstract definition) and then develop how to actually get that from _normal_, continuous functions.

Re: Notes on Lagrange Interpolating Polynomials

#14

Post by max_likelihood » Tue, Mar 03, 2026, 6:21 PM UTC

Thank you for sharing. One thing I found confusing was the introduction of l_{i}'(x). I kept thinking this was short for \frac{d}{dx} l_{i}(x), but it's not the derivative!