Solutions to Nonlinear Equations: Difference between revisions
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== Parameters == | == Parameters == | ||
$\epsilon$: (additive) tolerance error | |||
$a, b$: endpoint values, with $b>a$ | |||
$n_{max}$: maximum number of iterations$ | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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|- | |- | ||
| [[Bisection method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Bisection method]] || -150 || $O( | | [[Bisection method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Bisection method]] || -150 || $O(n_{max})$ || $O({1})$ || Exact || Deterministic || | ||
|- | |- | ||
| [[Regula Falsi method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Regula Falsi method]] || -200 || $O( | | [[Regula Falsi method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Regula Falsi method]] || -200 || $O(n_{max})$ || $O({1})$ || Exact || Deterministic || | ||
|- | |- | ||
| [[Secant method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Secant method]] || -1400 || $O( | | [[Secant method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Secant method]] || -1400 || $O(n_{max})$ || $O({1})$ || Exact || Deterministic || | ||
|- | |- | ||
| [[Newton's method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Newton's method]] || 1669 || $O( | | [[Newton's method (Solutions to Nonlinear Equations Solutions to Nonlinear Equations)|Newton's method]] || 1669 || $O(n_{max})$ || $O({1})$ || Exact || Deterministic || | ||
|- | |- | ||
|} | |} | ||
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[[File:Solutions to Nonlinear Equations - Time.png|1000px]] | [[File:Solutions to Nonlinear Equations - Time.png|1000px]] | ||
Latest revision as of 09:12, 28 April 2023
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
