Search for a tool
Neville Interpolating Polynomial

Tool to find a curve equation via the Neville-Aikten algorithm. The Neville interpolating polynomial method is a polynomial approximation to obtain the equation of a curve by knowing some coordinates of it.

Results

Neville Interpolating Polynomial -

Tag(s) : Functions

Share
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 Neville Interpolating Polynomial tool, so feel free to write! Thank you !

Neville Interpolating Polynomial

Interpolation of Polynomial by Neville


Loading...
(if this message do not disappear, try to refresh this page)

Extrapolation


Tool to find a curve equation via the Neville-Aikten algorithm. The Neville interpolating polynomial method is a polynomial approximation to obtain the equation of a curve by knowing some coordinates of it.

Answers to Questions

How to find the equation of a curve using Neville algorithm?

dCode implement the method of Neville for Polynomial interpolation to find an equation by knowing some of its points $ (x_i, y_i) $.

Example: Points (0,0),(2,4),(4,16) can be interpolated to find the original equation : x^2

The interpolated polynomial is calculated by the Neville algorithm for n distinct points. (This algorithm can be represented as a pyramid, at each step a term disappears until having a single final result).

- Create polynomials $ P_i $ of degree 0 for each point $ x_i, y_i $ with $ i = 1,2,...,n $, this is equivalent to $ P_i (x) = y_i $.

Example: $ P_1 = 0 $, $ P_2 = 4 $, $ P_3 = 16 $

- For each consecutive $ P_i $ and $ P_j $ calculate $$ P_{ij}(x) = \frac{(x_j-x)P_i(x) + (x-x_i)P_j(x)}{x_j-x_i} $$

Example: $ P_{12} = \frac{(2-x)0 + (x-0)4}{2-0} = 2x $, $ P_{23} = \frac{(4-x)4 + (x-2)16}{4-2} = \frac{16-4x+16x-32}{2} = 6x-8 $

- Repeat this last step until having a single polynomial.

Example: $ P_{1(2)3} = \frac{(4-x)(2x) + (x-0)(6x-8)}{4-0} = \frac{8x-2x^2 + 6x^2 -8x}{4} = x^2 $

What are the limits for Interpolating with Neville?

Calculations are costful so the program is limited to 25 points with distinct x-coordinate in the set Q.

Source code

dCode retains ownership of the online 'Neville 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 Neville Interpolating Polynomial download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

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


Source : https://www.dcode.fr/neville-interpolating-polynomial
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback