Bisection Method

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/**
*
* @file
* @brief Find real roots of a function in a specified interval [a, b], where f(a)*f(b) < 0
*
* @details Given a function f(x) and an interval [a, b], where f(a) * f(b) < 0, find an approximation of the root
* by calculating the middle m = (a + b) / 2, checking f(m) * f(a) and f(m) * f(b) and then by choosing the
* negative product that means Bolzano's theorem is applied,, define the new interval with these points. Repeat until
* we get the precision we want [Wikipedia](https://en.wikipedia.org/wiki/Bisection_method)
*
* @author [ggkogkou](https://github.com/ggkogkou)
*
*/

const findRoot = (a, b, func, numberOfIterations) => {
// Check if a given  real value belongs to the function's domain
const belongsToDomain = (x, f) => {
const res = f(x)
return !Number.isNaN(res)
}
if (!belongsToDomain(a, func) || !belongsToDomain(b, func))
throw Error("Given interval is not a valid subset of function's domain")

// Bolzano theorem
const hasRoot = (a, b, func) => {
return func(a) * func(b) <= 0
}
if (hasRoot(a, b, func) === false) {
throw Error(
'Product f(a)*f(b) has to be negative so that Bolzano theorem is applied'
)
}

// Declare m
const m = (a + b) / 2

// Recursion terminal condition
if (numberOfIterations === 0) {
return m
}

// Find the products of f(m) and f(a), f(b)
const fm = func(m)
const prod1 = fm * func(a)
const prod2 = fm * func(b)

// Depending on the sign of the products above, decide which position will m fill (a's or b's)
if (prod2 <= 0) return findRoot(m, b, func, --numberOfIterations)

return findRoot(a, m, func, --numberOfIterations)
}

export { findRoot }