Bisect {CooccurrenceAffinity}

Bisections for finding a root of a function

Description

Find a root of a function by the method of Bisections

Usage

Bisect(ffnc, intrv, tol = 1e-08)

Arguments

ffnc

an increasing function of a single scalar argument

intrv

an interval over which the root of ffnc is sought

tol

a tolerance determining when the successive bisections of the interval within which the root will lie have become small enough to stop

Details

This function finds the root of the increasing function ffnc over the scalar interval intrv by the Method of Bisections. The function must be increasing but need not be smooth, and it must have a negative sign (value less than -tol) at the left endpoint of intrv and positive sign (value greater than tol) at the right endpoint. The method of Bisection is used in successive iterations to successively halve the width of the interval in which the root lies.

Value

This function returns a vector consisting of two numbers. The first named root is an estimate of the root x solving ffnc(x) = 0, valid within an error of tol. The second output vector element named fval is the value of the function ffnc at root. It should be very close to 0 unless the function happens to jump from a value less than 0 to a value greater than 0 at root.

Author(s)

Eric Slud

References

to be added

Examples

Bisect(function(x) x^2-1, c(0,2),1e-8)