Tool to find the equation of a function. Lagrange Interpolating Polynomial is a method for finding the equation corresponding to a curve having some dots coordinates of it.

Lagrange Interpolating Polynomial - dCode

Tag(s) : Functions

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*!

Tool to find the equation of a function. Lagrange Interpolating Polynomial is a method for finding the equation corresponding to a curve having some dots coordinates of it.

Lagrange polynomials are computed using the formula :

$$ P(X)=\sum_{j=0}^n y_j \left(\prod_{i=0,i\neq j}^n \frac{X-x_i}{x_j-x_i} \right) $$

with $ P(X) $ the Lagrande polynomial and the dots $ (x_0, y_0),\dots,(x_n, y_n) $ and $ x_i $ distinct.

From the points whose coordinates are known, the lagrange polynomial calculator can thus predict other points based on the assumption that the curve formed by these points is derived from a polynomial equation.

dCode allow to use the Lagrangian method for **interpolating a Polynomial** and finds back the original equation using known points (x,y) values.

__Example:__ By the knowledge of the points $ (x,y) $ : $ (0,0),(2,4),(4,16) $ the Polynomial Lagrangian Interpolation method allow to find back the équation $ y = x^2 $. Once deducted, the interpolating function $ f(x) = x^2 $ allow to estimate the value for $ x = 3 $, here $ f(x) = 9 $.

The Lagrange interpolation method allows a good approximation of polynomial functions.

There are others interpolation formulas (rather than Lagrange/Rechner) such as Neville interpolation also available online on dCode.

Since the complexity of the calculations increases with the number of points, the program is limited to 25 coordinates (with distinct x-values in the rational number set Q).

dCode retains ownership of the source code of the script Lagrange 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 Lagrange Interpolating Polynomial script for offline use on PC, iPhone or Android, ask for price quote on contact page !

lagrange,interpolating,interpolation,equation,polynomial,curve,dot,value,function,rechner,lagrangian

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

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲