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.

Neville Interpolating Polynomial - dCode

Tag(s) : Mathematics

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

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.

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

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

dCode retains ownership of the source code of the script Neville Interpolating Polynomial online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the online Neville Interpolating Polynomial script for offline use, for you, your company or association, see you on contact page !

neville,aikten,interpolating,interpolation,equation,polynomial,curve,dot,value,function

Source : http://www.dcode.fr/neville-interpolating-polynomial

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode