Search for a tool
Newton Interpolating Polynomial

Tool to find the equation of a curve via Newton's algorithm. Newtonian interpolation is a polynomial approximation allowing to obtain the Lagrange polynomial as equation of the curve by knowing its points.

Results

Newton Interpolating Polynomial -

Tag(s) : Functions

Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our community Discord for help requests!

Thanks to your feedback and relevant comments, dCode has developped the best Newton Interpolating Polynomial tool, so feel free to write! Thank you !

# Newton Interpolating Polynomial

## Newtonian Interpolation Calculator

### Extrapolation

Tool to find the equation of a curve via Newton's algorithm. Newtonian interpolation is a polynomial approximation allowing to obtain the Lagrange polynomial as equation of the curve by knowing its points.

### How to find the equation of a curve using Newton algorithm?

dCode allows to use Newton's method for Polynomial Interpolation in order to find the equation of the polynomial (identical to Lagrange) in the Newton form.

From $n + 1$ known points $(x_i, y_i)$, the Newton form of the polynomial is equal to $$P(x)= [y_0] + [y_0,y_1] (x-x_0) + \ldots + [y_0,\ldots ,y_n] (x-x_0) \ldots (x-x_{n-1})$$

with the notation $[y_i]$ for divided difference.

Example: Curve whose points (1,3) and (2,5) are known. $$P(x) = [y_0] + [y_0,y_1] (x-x_0) \\ = 3 + \left(\frac{3}{1-2}+\frac{5}{2-1}\right) (x-1) = 3+2(x-1) = 2x+1$$

### What are the limits for Interpolating with Newton?

Newton Divided Differences are noted $[y_i]$ and computed by the formula $$[y_0,\dots ,y_k]=\sum_{j=0}^k {\frac{y_j}{\prod_{0\leq i\leq k,\,i\neq j}(x_j-x_i)}}$$

NB: If $k = 0$, then the product $\prod(x_j-x_i) = 1$ (empty product)

## Source code

dCode retains ownership of the online 'Newton Interpolating Polynomial' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Newton Interpolating Polynomial download for offline use on PC, tablet, iPhone or Android !

## Need Help ?

Please, check our community Discord for help requests!