alt Hacker NewsI believe the author assumes that it's clear to the reader that there is a distinction between how a mathematical object is defined, and how it's computationally used. A polynomial can be defined as a power series, but it's not how they are computationally used. In this sense, the author was mistaken.
But it's not that the problems are "circumvented", in the sense that it's a kind of a hack or a patch, but they are solved, in the sense that there is a systematic way to correctly compute with polynomials.
>But it's not that the problems are "circumvented", in the sense that it's a kind of a hack or a patch, but they are solved, in the sense that there is a systematic way to correctly compute with polynomials.
But the author does not even acknowledge that there is a wrong way. He claims that it is just a "MYTH" that polynomials have huge problems.
Read the article, nowhere does the author acknowledge that these numerical issues exist at all. Nowhere does the author talk about why the specific methods he uses work or even acknowledge that had he used a naive approach and written the polynomials as a power series over a large interval everything would have fallen apart.
Surely the "MYTH" that high degree polynomials are dangerous is not a myth. Concrete examples where naive approaches fail are trivially easy to find.
Again. I think you are missing the point entirely. I am not saying that these Fourier type projections are "wrong" or "bad" or "numerically unstable" or that you can't write an article about those or that high degree polynomials are impossible to work with.
I am saying that if you claim that it is a "MYTH" that high degree polynomials are dangerous, you should mention why people think that is the case and why your method works. Everything else seems totally disingenuous.