Solutions to Nonlinear Equations (Solutions to Nonlinear Equations)

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Compute the solutions to a given nonlinear equation of the form $f(x) = 0$.


$\epsilon$: (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

Solutions to Nonlinear Equations - Time.png