Sequential Evaluation of Polynomials If you don’t have any parallelism available, Horner’s scheme is a good option. And if you have the...
An Iterative Method Compute the minimax approximation in a wider format. Then round the coefficient of the constant term. Then recompute...
We discussed calculating the minimax polynomial using Remez’s Algorithm, but we overlooked some subtleties. While the algorithm does...
We never discussed how to calculate \(||f-p||_{\infty}\). Maple has a function to do this, but it can be inaccurate. Most people will...
Sometimes you need a fairly high degree polynomial to get reasonable accuracy, but can achieve a far greater accuracy with a much lower...
Remez’s algorithm is one that converges to the minimax polynomial of a function. The author recommends using a polynomial approximation...
Chebyshev vs Minimax Note that the best minimax polynomial approximation need not be the Chebyshev polynomial. The latter is the best...
The supremum norm is given by \(||f-p||_{\infty}=\max_{a\le x\le b}|f(x)-p(x)|\). It is denoted by \(L^{\infty}\). Given a function...
First, just a definition: A monic polynomial is one whose leading coefficient is 1. We want to find a polynomial of degree \(n\) that...
We often will approximate functions as polynomial or rational functions. When doing this, we introduce two types of errors:...