General Root Computation (Root Computation)
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Description
Given a real continuous function, compute one of the roots.
Related Problems
Related: Root Computation with continuous first derivative
Parameters
$\epsilon$: (additive) tolerance error
$a, b$: endpoint values, with $b>a$
$n_{max}$: maximum number of iterations
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Bisection method | 1820 | $O(n_{max})$ | $O({1})$ | epsilon, additive | Deterministic | |
| False position method | 1690 | $O(n_{max})$ | $O({1})$ | epsilon, additive | Deterministic | |
| Secant method | 1940 | $O(n_{max})$ | $O({1})$ | epsilon, additive | Deterministic | |
| Ridder's method | 1979 | $O(n_{max})$ | $O({1})$ | epsilon, additive | Deterministic | Time |
| Muller's method | 1956 | $O(n_{max})$ | $O({1})$ | epsilon, additive | Deterministic | Time |
| Illinois Algorithm | 1971 | $O(n_max)$ | $O({1})$ | epsilon, additive | Deterministic | Time |
| Anderson–Björck algorithm | 1973 | $O(n_max)$ | $O({1})$ | epsilon, additive | Deterministic | Time |
| ITP Method | 1940? | $O(n_0+log((b-a)$/epsilon)) | $O({1})$ | epsilon, additive | Deterministic | |
| Steffensen's method | 1940(?) | $O(n_max)$ | $O({1})$ | epsilon, additive | Deterministic | |
| Inverse quadratic interpolation | 1940(?) | $O(n_max)$ | $O({1})$ | epsilon, additive | Deterministic | |
| Brent-Dekker Method | 1973 | $O(n_max)$ | $O({1})$ | epsilon, additive | Deterministic | Time |