NLRoot (version 1.0)

SMfzero: Secant Method

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

Value

the root of the function

Details

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

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")
  }