Termination Condition
In addition to a routine for reducing the size of the bracketing of the solution, a complete algorithm must have a termination condition. The one provided in the book Numerical Recipes in C is based on testing the gaps among, and, terminating when within the relative accuracy bounds:
where is a tolerance parameter of the algorithm and is the absolute value of . The check is based on the bracket size relative to its central value, because that relative error in is approximately proportional to the squared absolute error in in typical cases. For that same reason, the Numerical Recipes text recommends that where is the required absolute precision of .
Read more about this topic: Golden Section Search
Famous quotes containing the words termination and/or condition:
“We hoped for a happy termination of this terrible war long before this; but God knows best, and has ruled otherwise.”
—Abraham Lincoln (1809–1865)
“Beautiful credit! The foundation of modern society. Who shall say that this is not the golden age of mutual trust, of unlimited reliance upon human promises? That is a peculiar condition of society which enables a whole nation to instantly recognize point and meaning in the familiar newspaper anecdote, which puts into the mouth of a distinguished speculator in lands and mines this remark:M”I wasn’t worth a cent two years ago, and now I owe two millions of dollars.””
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)