Solutions to Nonlinear Equations (Solutions to Nonlinear Equations)

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

Space Complexity Graph

Time-Space Tradeoff