Showing:

8.9K

20

2yrs ago

2

0

MIT

No

# newton-raphson-method

Find zeros of a function using Newton's Method

## Introduction

The Newton-Raphson method uses the tangent of a curve to iteratively approximate a zero of a function, f(x). This yields the update: ## Example

Consider the zero of (x + 2) * (x - 1) at x = 1:

var nr = require('newton-raphson-method');

function f (x) { return (x - 1) * (x + 2); }
function fp (x) { return (x - 1) + (x + 2); }

// Using the derivative:
nr(f, fp, 2)
// => 1.0000000000000000 (6 iterations)

// Using a numerical derivative:
nr(f, 2)
// => 1.0000000000000000 (6 iterations)


## Installation

\$ npm install newton-raphson-method


## API

#### require('newton-raphson-method')(f[, fp], x0[, options])

Given a real-valued function of one variable, iteratively improves and returns a guess of a zero.

Parameters:

• f: The numerical function of one variable of which to compute the zero.
• fp (optional): The first derivative of f. If not provided, is computed numerically using a fourth order central difference with step size h.
• x0: A number representing the intial guess of the zero.
• options (optional): An object permitting the following options:
• tolerance (default: 1e-7): The tolerance by which convergence is measured. Convergence is met if |x[n+1] - x[n]| <= tolerance * |x[n+1]|.
• epsilon (default: 2.220446049250313e-16 (double-precision epsilon)): A threshold against which the first derivative is tested. Algorithm fails if |y'| < epsilon * |y|.
• maxIterations (default: 20): Maximum permitted iterations.
• h (default: 1e-4): Step size for numerical differentiation.
• verbose (default: false): Output additional information about guesses, convergence, and failure.

Returns: If convergence is achieved, returns an approximation of the zero. If the algorithm fails, returns false.

Ricky Reusser

## Rate & Review

Great Documentation0
Easy to Use0
Performant0
Highly Customizable0
Bleeding Edge0
Responsive Maintainers0
Poor Documentation0
Hard to Use0
Slow0
Buggy0
Abandoned0
Unwelcoming Community0
100  No reviews found
Be the first to rate

## Alternatives  No alternatives found

## Tutorials  No tutorials found