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

Description Usage Arguments Value Author(s) References Examples

Finds roots of univariate functions by modifying the usual Newton-Raphson method by decreasing the step sizes when necessary.

1	damped.newton(fun, derf, x0, eps, maxit = 20, damp = seq(0, 40),silent=TRUE)

`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.
`damp`	a vector beginning from zero and increasing by one unit to decrease the step sizes.
`silent`	a logical statement which decides whether the iterations should be printed.

Returns a numeric result of the root.

Ozgur Asar, Ozlem Ilk

Bose, K. S. (2008). Numeric Computing in Fortran. Alpha Science.

Conte, S. D., de Boor, C. (1980). Elementary Numerical Analysis: An Algorithmic Approach, third edition. New York: McGraw-Hill Publications.

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

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f1=function(x) x^3+sqrt(x)-1
df1=function(x) 3*x^2+(1/2)*x^(-1/2)
damped.newton(f1,df1,2,10^-10,maxit=40,silent=FALSE)

Iteration: 1 ; Result= 1.318883
Iteration: 2 ; Result= 0.8868571
Iteration: 3 ; Result= 0.6656977
Iteration: 4 ; Result= 0.6085951
Iteration: 5 ; Result= 0.6054324
Iteration: 6 ; Result= 0.6054234
Solution: 0.6054234
[1] 0.6054234