In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data...

polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials. The original use of interpolation polynomials was...

numbers Lagrangian point, in physics and astronomy Lagrange polynomial Lagrangian mechanics Lagrange Bay, Western Australia La Grange (originally La Grange...

of p n ( z ) {\displaystyle p_{n}(z)} using the interpolating polynomials of Lagrange interpolation: I k ( z ) = ( z − z 0 ) ( z − z 1 ) ⋯ ( z − z k...

conjecture Polynomial decomposition, factorization under functional composition Delta operator Bernstein–Sato polynomial Lagrange polynomial Runge's phenomenon...

exploits the Lagrange interpolation theorem, specifically that k {\displaystyle k} points on the polynomial uniquely determines a polynomial of degree less...

method Lagrange number Lagrange point colonization Lagrange polynomial Lagrange property Lagrange reversion theorem Lagrange resolvent Lagrange spectrum...

from the Taylor series, they may be obtained by differentiating the Lagrange polynomials ℓ j ( ξ ) = ∏ i = 0 , i ≠ j k ξ − x i x j − x i , {\displaystyle...

In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a...

Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes...

after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues...

Companion matrix § Diagonalizability Schur polynomial – a generalization Alternant matrix Lagrange polynomial Wronskian List of matrices Moore determinant...

by a polynomial of degree k {\textstyle k} , called the k {\textstyle k} -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the...

. {\displaystyle m,n,q.} Horner's method Polynomial sequence Newton polynomial Lagrange polynomial Legendre polynomial Bernstein form Chebyshev form...

an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} , where P is a polynomial with coefficients in some...

In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate...

calculus Lagrange's trigonometric identities, two trigonometric identities Lagrange's four-square theorem, a theorem from number theory Lagrange polynomial for...

All-one polynomials Abel polynomials Bell polynomials Bernoulli polynomials Cyclotomic polynomials Dickson polynomials Fibonacci polynomials Lagrange polynomials...

L_{(n-1)i})} , with coordinates equal to the coefficients of the Lagrange polynomials L i ( x ) = L 0 i + L 1 i x + ⋯ + L ( n − 1 ) i x n − 1 = ∏ j ≠ i...

widely used than Lagrange's. Both bounds result from the Gershgorin circle theorem applied to the companion matrix of the polynomial and its transpose...

weighted mean of the vertex values, where the weights are the Lagrange interpolation polynomials. These weights also constitute a set of generalized barycentric...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

data symbols from 0 to k − 1 and sends them. He then constructs a (Lagrange) polynomial p(x) of order k such that p(i) is equal to data symbol i. He then...

In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse...

roots, originally in the form of Lagrange resolvents, later developed in Galois theory. Consider a monic polynomial in t of degree n P = t n + a n − 1...

numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician...

interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing...

resolvent invariant is linear in the roots. The Lagrange resolvent may refer to the linear polynomial ∑ i = 0 n − 1 X i ω i {\displaystyle \sum _{i=0}^{n-1}X_{i}\omega...

for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by...