# NIMfzero: Newton iteration method In NLRoot: searching for the root of equation

## Description

Newton iteration method to Find the Root of Nonlinear Equation.

## Usage

 `1` ```NIMfzero(f, f1, x0 = 0, num = 100, eps = 1e-05, eps1 = 1e-05) ```

## Arguments

 `f` the objective function which we will use to solve for the root `f1` the derivative of the objective function (say f) `x0` the initial value of Newton iteration method or Newton downhill method `num` the number of sections that the interval which from Brent's method devide into. num=100 when it is default `eps` the level of precision that |x(k+1)-x(k)| should be satisfied in order to get the idear real root. eps=1e-5 when it is default `eps1` the level of precision that |f(x)| should be satisfied, where x comes from the program. when it is not satisified we will fail to get the root

## Details

the root we found out is based on the x0. So it is better to choose x0 carefully

## Value

the root of the function

## Note

Maintainer:Zheng Sengui<[email protected]>

## Author(s)

Zheng Sengui,Lu Xufen,Hou Qiongchen,Zheng Jianhui

## References

Luis Torgo (2003) Data Mining with R:learning by case studies. LIACC-FEP, University of Porto

`BFfzero`,`NDHfzero`,`SMfzero`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ```f<-function(x){x^3-x-1};f1<-function(x){3*x^2-1}; NIMfzero(f,f1,0) ##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. ## The function is currently defined as function (f, f1, x0 = 0, num = 100, eps = 1e-05, eps1 = 1e-05) { a = x0 b = a - f(a)/f1(a) i = 0 while ((abs(b - a) > eps) & (i < num)) { a = b b = a - f(a)/f1(a) i = i + 1 } print(b) print(f(b)) if (abs(f(b)) < eps1) { print("finding root is successful") } else print("finding root is fail") } ```