SMfzero: Secant Method

In NLRoot: searching for the root of equation

Description

Secant Method to Find the Root of Nonlinear Equation.

Usage

SMfzero(f, x1, x2, num = 1000, eps = 1e-05, eps1 = 1e-05)

Arguments

f	the objective function which we will use to solve for the root
x1	the initial value of Secant Method
x2	the initial value of Secant Method
num	the number of sections that the interval which from Brent's method devide into. num=1000 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

Be careful to choose x1 & x2.if not we maybe fail to get the root

Value

the root of the function

Note

Maintainer:Zheng Sengui<[e-mail]>

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

See Also

BFfzero,NDHfzero,NIMfzero

Examples

f<-function(x){x^3-x-1};f1<-function(x){3*x^2-1};
SMfzero(f,0,2)


##---- 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, x1, x2, num = 1000, eps = 1e-05, eps1 = 1e-05) 
{
    i = 0
    while ((abs(x1 - x2) > eps) & (i < num)) {
        c = x2 - f(x2) * (x2 - x1)/(f(x2) - f(x1))
        x1 = x2
        x2 = c
        i = i + 1
    }
    print(x2)
    print(f(x2))
    if (abs(f(x2)) < eps1) {
        print("finding root is successful")
    }
    else print("finding root is fail")
  }

Example output

[1] 1.324718
[1] 4.412026e-13
[1] "finding root is successful"
function (f, x1, x2, num = 1000, eps = 1e-05, eps1 = 1e-05) 
{
    i = 0
    while ((abs(x1 - x2) > eps) & (i < num)) {
        c = x2 - f(x2) * (x2 - x1)/(f(x2) - f(x1))
        x1 = x2
        x2 = c
        i = i + 1
    }
    print(x2)
    print(f(x2))
    if (abs(f(x2)) < eps1) {
        print("finding root is successful")
    }
    else print("finding root is fail")
}

NLRoot documentation built on May 2, 2019, 7:31 a.m.