chebyshev

Chebyshev will tell you 75%), and even Chebyshev had to impose a restriction to get that bound--it assumes finite mean and variance.

But the Chebyshev polynomials, especially in their recursive definition, are a stroke of genius.

I'd just use a Chebyshev approximation transformed into a Padé approximation, then perturb the coefficients to optimize maximum error.

For instance, Chebyshev polynomials T_n enjoy an alternation property over their extremal points -- so in the Lagrange basis, in many problems (e.g.

The secret sauce is that Chebyshev approximation spreads the error as ripples across the function, rather than at its edges like with Taylor series approximation.

In DSP math, it is common to use Chebyshev polynomial approximation.

Similar issues turns up in transliterating Cyrillic -- Chebyshev vs Tschebyshev.

Wiggling feels more like a second-derivative thing to me but that's discussed too - Chebyshev polynomials max out the second derivative as well as the first.

Hastings provides Taylor series and Chebyshev polynomial approximations.

It's not a historical accident we use it everywhere, for example it naturally appears in the very useful Chebyshev inequality, and a million other contexts.

It's sometimes called Chebyshev approximation.

Noob DSP designers think 'even order harmonics!', so they slap a Chebyshev polynomial in the chain and half the time they don't even remember you have to oversample to avoid aliasing.

Based on those definitions, I would guess that “Chebyshev” distance is almost always the most accurate heuristic to use when you check “Allow Diagonal”, because it will always be perfectly accurate if there are no walls in the way, unlike the others.

"Discrete spaces, Bayes theorem and expected values" you can learn in a day, "Markovs, Chebyshev and Chernoff inequalities" are mostly only useful for further theoretical work, so is "the law of large numbers".

Also based on the Chebyshev's inequality, +2 std dev has a minimum percentile of 75%.

Not my field either but using (Chebyshev) polynomials to approximate _exponential functionals_ on [believably] infinite or scale-free graphs sounds rather interesting..

Chebyshev polynomials cos(n arcos(x)) provide one of the proofs that every continuous function f:[0,1]->R can be uniformly approximated by polynomial functions.