# funcBisec: Bisection function In informativeSCI: Informative Simultaneous Confidence Intervals

 funcBisec R Documentation

## 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.