Derivation of The Method
Starting with initial values and, we construct a line through the points and, as demonstrated in the picture on the right. In point-slope form, this line has the equation
We find the root of this line – the value of such that – by solving the following equation for :
The solution is
We then use this new value of as and repeat the process using and instead of and . We continue this process, solving for, etc., until we reach a sufficiently high level of precision (a sufficiently small difference between and ).
- ...
Read more about this topic: Secant Method
Famous quotes containing the word method:
“No method nor discipline can supersede the necessity of being forever on the alert. What is a course of history or philosophy, or poetry, no matter how well selected, or the best society, or the most admirable routine of life, compared with the discipline of looking always at what is to be seen? Will you be a reader, a student merely, or a seer? Read your fate, see what is before you, and walk on into futurity.”
—Henry David Thoreau (1817–1862)