Citation
Abstract
This article presents a mathematical root finder capable of finding all roots of an arbitrary continuous function within a given interval subject to very lenient parameterized assumptions, which are (1) that adjacent roots are separated at least by a given amount, xGuard; (2) any point whose function value is less than ff in magnitude is considered to be a root; (3) function values at distances xGuard away from a root are larger than ff, unless there is another root located in this vicinity; (4) a root is considered found if, during iteration, two root candidates differ by less than a prespecified fx; and (5) that the optimum cubic polynomial matching the function at the end and two internal points, and that is within a relative error fraction fL at its midpoint, is reliable in indicating whether the function has extrema within the interval. The robustness of this method depends solely on choosing these four parameters that control the search. The roots of discontinuous functions were also found, but at degraded performance.
Details
- Volume
- 42-176
- Published
- February 15, 2009
- Pages
- 1–14
- File Size
- 241.8 KB