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...

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

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

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...

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

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

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

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

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...

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

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

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...

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

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...

explicit formula for Lagrange inversion. The partial or incomplete exponential Bell polynomials are a triangular array of polynomials given by B n , k (...

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...

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...

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...

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

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...

the table above correspond to the latter definition. The theory of Lagrange polynomials provides explicit formulas for the finite difference coefficients...

an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} , where P is a polynomial, usually with rational numbers...

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

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

coefficients of the above interpolating polynomial. Expressing X ( z ) {\displaystyle X(z)} as the Lagrange polynomial of order N − 1 {\displaystyle N-1} ...

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...

point Lagrange reversion theorem Lagrange polynomial Lagrange's four-square theorem Lagrange's theorem Lagrange's theorem (group theory) Lagrange invariant...