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) : Functions

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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 costful 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, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Neville Interpolating Polynomial script for offline use on PC, iPhone or Android, ask for price quote on contact page !

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

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