Tag chebyshev

Remez’s Algorithm

Remez’s algorithm is one that converges to the minimax polynomial of a function. The author recommends using a polynomial approximation...

Miscellaneous (Chebyshev)

Chebyshev vs Minimax Note that the best minimax polynomial approximation need not be the Chebyshev polynomial. The latter is the best...

Least Maximum Polynomial Approximations

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...

Least Squares Polynomial Approximations

First, just a definition: A monic polynomial is one whose leading coefficient is 1. We want to find a polynomial of degree \(n\) that...

Methods of Point Estimation

\(\newcommand{\Cov}{\mathrm{Cov}}\) \(\newcommand{\Corr}{\mathrm{Corr}}\) \(\newcommand{\Sample}{X_{1},\dots,X_{n}}\) The Method...

Continuous Random Variables and Probability Distributions

Continuous distributions are given by a probability density function (pdf): \begin{equation*} P\left(a\le X\le...

Discrete Random Variables

Random Variables A discrete random variable is one whose set of possible values is countable. Probability Distributions for Discrete...