newton.rapheson {elliptic} | R Documentation |
Newton Rapheson iteration to find roots of equations with the emphasis on complex functions
newton.rapheson(initial, f, fdash, maxiter, tol = .Machine$double.eps)
initial |
Starting guess |
f |
Function for which f(z)=0 is to be solved for z |
fdash |
Derivative of function (note: Cauchy-Riemann conditions assumed) |
maxiter |
Maximum number of iterations attempted |
tol |
Tolerance: iteration stops if |f(z)|<tol |
Bog-standard
Returns z with |f(z)|<tol
Robin K. S. Hankin
#Find the two square roots of 2+i: f <- function(z){z^2-(2+1i)} fdash <- function(z){2*z} newton.rapheson( 1.4+0.3i,f,fdash,maxiter=10) newton.rapheson(-1.4-0.3i,f,fdash,maxiter=10) #Now find the three cube roots of unity: g <- function(z){z^3-1} gdash <- function(z){3*z^2} newton.rapheson(-0.5+1i,g,gdash,maxiter=10) newton.rapheson(-0.5-1i,g,gdash,maxiter=10) newton.rapheson(+0.5+0i,g,gdash,maxiter=10)