Solutions to Nonlinear Equations (Solutions to Nonlinear Equations)
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Description
Compute the solutions to a given nonlinear equation of the form $f(x) = 0$.
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 | -150 | $O(n_{max})$ | $O({1})$ | Exact | Deterministic | |
| Regula Falsi method | -200 | $O(n_{max})$ | $O({1})$ | Exact | Deterministic | |
| Secant method | -1400 | $O(n_{max})$ | $O({1})$ | Exact | Deterministic | |
| Newton's method | 1669 | $O(n_{max})$ | $O({1})$ | Exact | Deterministic |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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