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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Neville Interpolating Polynomial
Interpolation of Polynomial by Neville
Answers to Questions (FAQ)
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.
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