funcBisec: Bisection function

In informativeSCI: Informative Simultaneous Confidence Intervals

Bisection function

Description

Bisection function to find solutions of the key equation of the informSCI-algorithm.

Usage

funcBisec(f_1, f_2, a, b, maxIter = 1000, tol = 1/10^3)

Arguments

f_1	Left side of the key equation as a function in one variable.
f_2	Right side of the key equation as a function in one variable.
a	A real value indicating the left bound of the search region. f_1(a)\leq f_2(a) must hold true.
b	A real value indicating the right bound of the search region. f_1(b)\geq f_2(b) must hold true.
maxIter	A positive integer defining the maximum number of iterations.
tol	A non-negative numeric indicating the error tolerance.

Details

The function tries to find a solution of the key equation of the informSCI-algorithm which is equivalent to determining the intersection point of f_1 and f_2. The function uses the bisection method and tries to determine the root of the function f_1-f_2. Note that by definition of the key equation and the assumptions of the informSCI-algorithm f_1-f_2 is a continuous strictly increasing function. Because of the assumptions on a and b f_1-f_2 has a non-positive function value in point a and non-negative function value in point b. Thus, f_1-f_2 has exactly one root in the closed interval [a,b].

The bisection method repeatedly halves the interval between a and b. The function stops when the root is found or when the maximum number of iterations is reached or when the interval is less than tol.

Value

Returns intersection point. In the case that no intersection point is found, the left side of the final interval is returned, rather than the midpoint. The returned point is a lower approximation of the solution of the key equation.

informativeSCI documentation built on June 22, 2024, 10:01 a.m.