In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data...
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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...
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conjecture Polynomial decomposition, factorization under functional composition Delta operator Bernstein–Sato polynomial Lagrange polynomial Runge's phenomenon...
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polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials. The original use of interpolation polynomials was...
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numbers Lagrangian point, in physics and astronomy Lagrange polynomial Lagrangian mechanics Lagrange Bay, Western Australia La Grange (originally La Grange...
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exploits the Lagrange interpolation theorem, specifically that k {\displaystyle k} points on the polynomial uniquely determines a polynomial of degree less...
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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...
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method Lagrange number Lagrange point colonization Lagrange polynomial Lagrange property Lagrange reversion theorem Lagrange resolvent Lagrange spectrum...
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Sylvester's formula (redirect from Lagrange–Sylvester interpolation)
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...
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Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes...
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All-one polynomials Abel polynomials Bell polynomials Bernoulli polynomials Cyclotomic polynomials Dickson polynomials Fibonacci polynomials Lagrange polynomials...
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In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then |H| is a divisor of |G|, i.e....
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Monomial basis (redirect from Polynomial basis)
. {\displaystyle m,n,q.} Horner's method Polynomial sequence Newton polynomial Lagrange polynomial Legendre polynomial Bernstein form Chebyshev form...
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calculus Lagrange's trigonometric identities, two trigonometric identities Lagrange's four-square theorem, a theorem from number theory Lagrange polynomial for...
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Companion matrix § Diagonalizability Schur polynomial – a generalization Alternant matrix Lagrange polynomial Wronskian List of matrices Moore determinant...
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widely used than Lagrange's. Both bounds result from the Gershgorin circle theorem applied to the companion matrix of the polynomial and its transpose...
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Algebraic equation (redirect from Polynomial equation)
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...
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Taylor's theorem (redirect from Lagrange error bound)
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...
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In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...
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Wilkinson's polynomial is a specific polynomial which was used by James H. Wilkinson in 1963 to illustrate a difficulty when finding the root of a polynomial: the...
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In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate...
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weighted mean of the vertex values, where the weights are the Lagrange interpolation polynomials. These weights also constitute a set of generalized barycentric...
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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...
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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...
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interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing...
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of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...
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Erasure code (section Polynomial oversampling)
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...
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numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician...
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In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse...
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In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...
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