newton: A function to find the roots of univariate functions.
In OOmisc: Ozgur-Ozlem Miscellaneous

Description Usage Arguments Details Value Author(s) References Examples

Finds roots of univariate functions by the usual Newton-Raphson (N-R) method.

1	newton(fun, derf, x0, eps, maxit = 20, silent = TRUE, tun=1)

`fun`	a function for which the root is searched.
`derf`	a function which is the first derivative of the function to be solved.
`x0`	a numeric value to be used to start the algorithm.
`eps`	a numeric value to be considered as the tolerance for convergence of the algorithm.
`maxit`	a numeric value which denotes maximum number of iterations to be consumed.
`silent`	a logical statement which decides whether the iterations should be printed.
`tun`	a numeric value to decrease the steps

tun is used to decrease the N-R steps, since it sometimes might miss the root value by taking large steps. tun=1 corresponds to usual N-R.

Returns a numeric result of the root.

Ozlem Ilk, Ozgur Asar

Ilk, O. (2011). R Yazilimina Giris [Introduction to R Language]. ODTU Yayincilik [METU Press].

# function and the derivative
f1=function(x) x^3+sqrt(x)-1
df1=function(x) 3*x^2+(1/2)*x^(-1/2)
# searching for a reasonable initial
x0=seq(0,2,,100)
plot(x0,f1(x0),type="n")
lines(x0,f1(x0))
abline(h=0,lty=2)
newton(f1,df1,0.5,10**-10,silent=FALSE)

Iteration: 1 , Result= 0.6152237
Iteration: 2 , Result= 0.6055087
Iteration: 3 , Result= 0.6054234
Iteration: 4 , Result= 0.6054234
Solution: 0.6054234
[1] 0.6054234