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.
All labels observed (6)
How this entity was disambiguated
This entity first appeared as the object of triple T6800909 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Newton interpolation polynomial Context triple: [Lagrange interpolation polynomial, relatedTo, Newton interpolation polynomial]
-
A.
Lagrange interpolation polynomial
The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
-
B.
Hermite interpolation
Hermite interpolation is a numerical analysis method for constructing a polynomial that matches both function values and specified derivatives at given data points.
-
C.
DPOLY
DPOLY is the American Physical Society’s Division of Polymer Physics, a professional unit focused on advancing research and knowledge in polymer science and related fields.
-
D.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
E.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Newton interpolation polynomial Target entity description: 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.
-
A.
Lagrange interpolation polynomial
The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
-
B.
Hermite interpolation
Hermite interpolation is a numerical analysis method for constructing a polynomial that matches both function values and specified derivatives at given data points.
-
C.
DPOLY
DPOLY is the American Physical Society’s Division of Polymer Physics, a professional unit focused on advancing research and knowledge in polymer science and related fields.
-
D.
Bernstein polynomials
Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
-
E.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
- F. None of above. chosen
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 ⓘ |
| 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
ⓘ
linked to:
Newton interpolation polynomial
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
ⓘ
linked to:
Newton interpolation polynomial
Newton forward interpolation formula ⓘ
linked to:
Newton interpolation polynomial
|
| namedAfter | Isaac Newton ⓘ |
| relatedTo |
Hermite interpolation
ⓘ
Lagrange interpolation polynomial ⓘ 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Newton interpolation polynomial Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Newton interpolation polynomial
linked to: Newton interpolation polynomial
linked to: Newton interpolation polynomial
linked to: Newton interpolation polynomial
linked to: Newton interpolation polynomial