Hermite interpolation
E502191
Hermite interpolation is a numerical analysis method for constructing a polynomial that matches both function values and specified derivatives at given data points.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Hermite spline | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
interpolation method
ⓘ
numerical analysis method ⓘ polynomial interpolation ⓘ |
| advantage |
can achieve higher accuracy with fewer nodes than Lagrange interpolation
ⓘ
incorporates derivative information to improve approximation quality ⓘ |
| application |
computer graphics
ⓘ
curve design ⓘ data fitting with derivative information ⓘ numerical solution of differential equations ⓘ |
| appliesTo |
complex-valued functions
ⓘ
real-valued functions ⓘ |
| assumes | function is sufficiently differentiable at interpolation points ⓘ |
| canBeExtendedTo |
Hermite splines
NERFINISHED
ⓘ
piecewise Hermite interpolation ⓘ |
| canBeFormulatedAs |
Hermite interpolation polynomial in Lagrange-like form
ⓘ
Hermite interpolation polynomial in Newton form ⓘ |
| comparedTo | Lagrange interpolation in terms of error behavior ⓘ |
| ensuresAtNodes |
equality of function values
ⓘ
equality of specified derivatives up to given order ⓘ |
| field |
approximation theory
ⓘ
numerical analysis ⓘ |
| generalizes | Lagrange interpolation ⓘ |
| goal |
construct a polynomial that matches function values at given points
ⓘ
construct a polynomial that matches specified derivatives at given points ⓘ |
| hasConcept | Hermite basis polynomials NERFINISHED ⓘ |
| hasErrorTerm | error expressed using higher-order derivative of the function ⓘ |
| hasSpecialCase | cubic Hermite interpolation ⓘ |
| input |
data points with derivative values
ⓘ
data points with function values ⓘ |
| isTaughtIn |
approximation theory courses
ⓘ
undergraduate numerical analysis courses ⓘ |
| limitation |
construction cost increases with number of derivatives
ⓘ
requires derivative values at interpolation points ⓘ |
| mathematicalNature | local polynomial approximation around multiple points ⓘ |
| namedAfter | Charles Hermite NERFINISHED ⓘ |
| output | interpolating polynomial ⓘ |
| property | interpolating polynomial is unique for given data and derivative conditions ⓘ |
| relatedTo |
Lagrange interpolation
ⓘ
Taylor polynomial ⓘ cubic Hermite spline ⓘ spline interpolation ⓘ |
| requires | solution of linear system for polynomial coefficients in some formulations ⓘ |
| typicalOrder | depends on number of points and derivative conditions ⓘ |
| usedIn |
finite element methods
ⓘ
geometric modeling ⓘ keyframe animation ⓘ |
| uses |
divided differences
ⓘ
polynomials ⓘ repeated nodes in divided differences ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hermite spline