newton_raphson {elliptic} R Documentation

## Newton Raphson iteration to find roots of equations

### Description

Newton-Raphson iteration to find roots of equations with the emphasis on complex functions

### Usage

 newton_raphson(initial, f, fdash, maxiter, give=TRUE, tol = .Machine\$double.eps)


### Arguments

 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 give Boolean, with default TRUE meaning to give output based on that of uniroot() and FALSE meaning to return only the estimated root tol Tolerance: iteration stops if |f(z)|

### Details

Bog-standard implementation of the Newton-Raphson algorithm

### Value

If give is FALSE, returns z with |f(z)|<tol; if TRUE, returns a list with elements root (the estimated root), f.root (the function evaluated at the estimated root; should have small modulus), and iter, the number of iterations required.

### Note

Previous versions of this function used the misspelling “Rapheson”.

### Author(s)

Robin K. S. Hankin

### Examples


# Find the two square roots of 2+i:
f <- function(z){z^2-(2+1i)}
fdash <- function(z){2*z}
newton_raphson( 1.4+0.3i,f,fdash,maxiter=10)
newton_raphson(-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_raphson(-0.5+1i,g,gdash,maxiter=10)
newton_raphson(-0.5-1i,g,gdash,maxiter=10)
newton_raphson(+0.5+0i,g,gdash,maxiter=10)
`

[Package elliptic version 1.4-0 Index]