Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Interpolation method
Polynomial |
| gptkbp:application |
gptkb:Computer_graphics
gptkb:signal_processing Cryptography Coding theory Numerical integration Numerical differentiation |
| gptkbp:category |
Multivariate polynomial interpolation
Univariate polynomial interpolation |
| gptkbp:component |
Lagrange basis polynomial
|
| gptkbp:degree |
n (for n+1 points)
|
| gptkbp:field |
gptkb:Mathematics
Numerical analysis |
| gptkbp:firstDescribed |
1795
|
| gptkbp:form |
L(x) = Σ_{j=0}^n y_j l_j(x)
|
| gptkbp:generalizes |
gptkb:Hermite_interpolation
Barycentric Lagrange interpolation |
| https://www.w3.org/2000/01/rdf-schema#label |
Lagrange polynomial
|
| gptkbp:limitation |
gptkb:Runge's_phenomenon
Computationally expensive for large n |
| gptkbp:namedAfter |
gptkb:Joseph-Louis_Lagrange
|
| gptkbp:property |
Passes through given data points
Unique for given set of points |
| gptkbp:relatedTo |
gptkb:Newton_polynomial
Finite differences |
| gptkbp:usedFor |
Polynomial interpolation
Approximating functions |
| gptkbp:bfsParent |
gptkb:Lagrange
|
| gptkbp:bfsLayer |
6
|