Chebyshev Polynomials
Chebyshev Coefficients for Chebyshev polynomials of the first kind.
chebCoeff(fun, a, b, n)
fun |
function to be approximated. |
a, b |
endpoints of the interval. |
n |
an integer |
For a function fun on on the interval [a, b] determines the
coefficients of the Chebyshev polynomials up to degree n that will
approximate the function (in L2 norm).
Vector of coefficients for the Chebyshev polynomials, from low to high degrees (see the example).
See the “Chebfun Project” <https://www.chebfun.org/> by Nick Trefethen.
Weisstein, Eric W. “Chebyshev Polynomial of the First Kind." From MathWorld — A Wolfram Web Resource. https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html
## Chebyshev coefficients for x^2 + 1
n <- 4
f2 <- function(x) x^2 + 1
cC <- chebCoeff(f2, -1, 1, n) # 3.0 0 0.5 0 0
cC[1] <- cC[1]/2 # correcting the absolute Chebyshev term
# i.e. 1.5*T_0 + 0.5*T_2
cP <- chebPoly(n) # summing up the polynomial coefficients
p <- cC %*% cP # 0 0 1 0 1Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.