updown function

Solve a simple equation using a step halving algorithm.

Solves equations of form $f(x)=0$, for scalar $x$ $(l<=x<=u)$ using a simple step halving algorithm, where $f(x)$ is a monotonic continuous function. Initial finite upper and lower bounds for x are required. The algorithm first computes $f$ for $x=u$ and $x=l$. If the sign was different then another call is performed at the midpoint $x=(u+l)/2$, and the midpoint is taken as a new upper or lower bound, according to the location of sign change. The upper or lower bound are repeatedly updated until the absolute value of f at the midpoint is below a specified criteria.

updown(l, u, fn, crit = 6)

Arguments

• l: The initial lower bound
• u: The initial upper bound
• fn: R-function for $f(x)$
• crit: The convergence criteria (Maximum accepted value of f at the solution is $10^{-\code{crit}}$).

Returns

A scalar giving the value of $x$ at the solution. If the sign did not change between l and u, NA is returned.

Author(s)

Lauri Mehtatalo <lauri.mehtatalo@uef.fi >

Warning

May lead to infinite loop for non-continuous functions. Works only with monotonic functions.

Examples

## Compute the median of Weibull distibution
fn<-function(x) pweibull(x,5,15)-0.5
updown(1,50,fn)