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# npm

## richardson-extrapolation

1.0.3 • Public • Published

# richardson-extrapolation

Use Richardson Extrapolation sequence acceleration to compute the order of convergence and exact value of a sequence

## Introduction

Richardson Extrapolation is a numerical method that uses solutions at multiple values of a small parameter (think: = grid size) to accelerate the converenge of a sequence. To make that concrete, consider an method that approximates the value of . Writing this as

the unknowns are the exact value , the error constant , and the order of convergence .

In its current form, this module solves for two of three unknowns using the solution at two parameter sizes . So for example, given the the order of convergence , you may approximate the exact value (with error of order ), or given the exact value , you may solve for the order of convergence .

The solution of all three unknowns requires the solution of a set of three nonlinear equations and is not implemented yet. :(

## API

#### require('richardson-extrapolation')( func, h, knowns )

Arguments:

• func: a function that takes small parameter as its only argument
• h: either a starting parameter size or a set of parameter sizes
• if a number, then is subdivided by a factor of 2 as needed t solve for the unknowns
• if an array of numbers, then the first are used as values of in order solve for unknowns
• knowns: a hash of known parameters. Possibilities are:
• provided (solves for and )
• provided (solves for and )

Returns: A hash containing three values: the approximated exact value , order of convergence , and the constant of the error term .

## TODO

Implement nonlinear simultaneous equation solver as a separate module in order to solve for all three unknowns.

## Credits

(c) 2015 Ricky Reusser. MIT License

## Keywords

### Install

npm i richardson-extrapolation

6

1.0.3