Taylor Series Approximation
Local polynomial approximation through Taylor series.
taylor(f, x0, n = 4, ...)
f |
differentiable function. |
x0 |
point where the series expansion will take place. |
n |
Taylor series order to be used; should be |
... |
more variables to be passed to function |
Calculates the first four coefficients of the Taylor series through numerical differentiation and uses some polynomial ‘yoga’.
Vector of length n+1 representing a polynomial of degree n.
TODO: Pade approximation.
taylor(sin, 0, 4) #=> -0.1666666 0.0000000 1.0000000 0.0000000
taylor(exp, 1, 4) #=> 0.04166657 0.16666673 0.50000000 1.00000000 1.00000000
f <- function(x) log(1+x)
p <- taylor(f, 0, 4)
p # log(1+x) = 0 + x - 1/2 x^2 + 1/3 x^3 - 1/4 x^4 +- ...
# [1] -0.250004 0.333334 -0.500000 1.000000 0.000000
## Not run:
x <- seq(-1.0, 1.0, length.out=100)
yf <- f(x)
yp <- polyval(p, x)
plot(x, yf, type = "l", col = "gray", lwd = 3)
lines(x, yp, col = "red")
grid()
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.