Newton interpolation polynomial
E620656
The Newton interpolation polynomial is a form of the interpolating polynomial that uses divided differences and a nested (incremental) structure, making it efficient to update when new data points are added.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
interpolating polynomial
ⓘ
mathematical concept ⓘ numerical analysis method ⓘ |
| advantage |
can be evaluated efficiently using nested multiplication
ⓘ
easier to update when adding new interpolation points ⓘ reuses previously computed divided differences ⓘ |
| appliesTo | distinct interpolation nodes ⓘ |
| basedOn | divided differences ⓘ |
| coefficientComputedBy |
first-order divided differences
ⓘ
higher-order divided differences ⓘ |
| coefficientNotation |
f[x_0, x_1, ..., x_k]
ⓘ
f[x_0] ⓘ |
| coefficientNotation | f[x_0, x_1] ⓘ |
| degree | at most n for n+1 data points ⓘ |
| domain |
complex-valued functions
ⓘ
real-valued functions ⓘ |
| errorDependsOn |
(n+1)th derivative of the interpolated function
ⓘ
product (x - x_0)...(x - x_n) ⓘ |
| evaluatedBy | Horner-like scheme ⓘ |
| hasAdvantageOver | Lagrange interpolation polynomial NERFINISHED ⓘ |
| hasCharacteristic |
efficiently updatable with new data points
ⓘ
incremental structure ⓘ nested form ⓘ numerically stable for well-ordered nodes ⓘ suitable for sequential data insertion ⓘ |
| hasComponent |
Newton basis polynomials
NERFINISHED
ⓘ
divided difference coefficients ⓘ |
| hasForm | p(x) = a_0 + a_1(x - x_0) + a_2(x - x_0)(x - x_1) + ... + a_n(x - x_0)...(x - x_{n-1}) ⓘ |
| hasVariant |
Newton backward interpolation formula
NERFINISHED
ⓘ
Newton forward interpolation formula NERFINISHED ⓘ |
| namedAfter | Isaac Newton NERFINISHED ⓘ |
| relatedTo |
Hermite interpolation
NERFINISHED
ⓘ
Lagrange interpolation polynomial NERFINISHED ⓘ finite difference methods ⓘ |
| satisfiesProperty |
passes through all given data points
ⓘ
unique interpolating polynomial for given nodes and values ⓘ |
| taughtIn |
approximation theory courses
ⓘ
numerical analysis courses ⓘ |
| usedFor |
approximating functions from discrete data
ⓘ
constructing an interpolating polynomial through given data points ⓘ polynomial interpolation ⓘ |
| usedIn |
computer graphics
ⓘ
data fitting ⓘ engineering approximation problems ⓘ scientific computing ⓘ |
| usesSequence |
function values f(x_0), f(x_1), ..., f(x_n)
ⓘ
nodes x_0, x_1, ..., x_n ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.