secantMethod

constexpr Complex secantMethod(Complex (*f)(Complex), const Complex &z0, const double alpha, const int epochs) noexcept: Performs the secant method algortihm on a complex function.

Parameters

Complex (*f)(Complex)

The function to root-find.

const Complex &z0

The first starting point.

const Complex &z1

The second starting point.

const int epochs

The number of iterations.

Returns

type Complex

A complex number.

This function root-finds the given complex function \(f\) using the following update rule:

\[z_{k+1} = z_k - f(z_k)\frac{z_k - z_{k - 1}}{f(z_k) - f(z_{k - 1})}\]

Example

auto fn = [](Complex z) { return sin(z); };
Complex z = secantMethod(fn, 0.1, 0.05, 1000);
std::cout << z << "\n";
std::cout << sin(z) << "\n";

Output:

-4.94066e-323 + 0j
-4.94066e-323 + 0j

References