Behaviour
The asymptotic behaviour is very good: generally, the iterates xn converge fast to the root once they get close. However, performance is often quite poor if you do not start very close to the actual root. For instance, if by any chance two of the function values fn−2, fn−1 and fn coincide, the algorithm fails completely. Thus, inverse quadratic interpolation is seldom used as a stand-alone algorithm.
The order of this convergence is approximately 1.8, it can be proved by the Secant Method analysis.
Read more about this topic: Inverse Quadratic Interpolation
Famous quotes containing the word behaviour:
“The methodological advice to interpret in a way that optimizes agreement should not be conceived as resting on a charitable assumption about human intelligence that might turn out to be false. If we cannot find a way to interpret the utterances and other behaviour of a creature as revealing a set of beliefs largely consistent and true by our standards, we have no reason to count that creature as rational, as having beliefs, or as saying anything.”
—Donald Davidson (b. 1917)
“The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
—Aldous Huxley (1894–1963)
“When we read of human beings behaving in certain ways, with the approval of the author, who gives his benediction to this behaviour by his attitude towards the result of the behaviour arranged by himself, we can be influenced towards behaving in the same way.”
—T.S. (Thomas Stearns)