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38 relations: Bernstein polynomial, Carlson's theorem, Chebfun, Chebyshev nodes, Chinese remainder theorem, Cryptography, Degree of a polynomial, Digital signal processing, Digital waveguide synthesis, Divided differences, Edward Waring, Finite difference coefficient, Finite field, Finite impulse response, Frobenius covariant, Horner's method, Identity matrix, Joseph-Louis Lagrange, Kronecker delta, Lebesgue constant (interpolation), Leonhard Euler, Linear algebra, Linear combination, Monomial basis, Neville's algorithm, Newton polynomial, Newton–Cotes formulas, Numerical analysis, Numerical integration, Philosophical Transactions of the Royal Society, Physical modelling synthesis, Polynomial interpolation, Runge's phenomenon, Shamir's Secret Sharing, Society for Industrial and Applied Mathematics, Sylvester's formula, Table of Newtonian series, Vandermonde matrix.
Bernstein polynomial
In the mathematical field of numerical analysis, a Bernstein polynomial, named after Sergei Natanovich Bernstein, is a polynomial in the Bernstein form, that is a linear combination of Bernstein basis polynomials.
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Carlson's theorem
In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson.
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Chebfun
Chebfun is a free/open-source software system written in MATLAB for numerical computation with functions of a real variable.
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Chebyshev nodes
In numerical analysis, Chebyshev nodes are specific real algebraic numbers, namely the roots of the Chebyshev polynomials of the first kind.
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Chinese remainder theorem
The Chinese remainder theorem is a theorem of number theory, which states that if one knows the remainders of the Euclidean division of an integer by several integers, then one can determine uniquely the remainder of the division of by the product of these integers, under the condition that the divisors are pairwise coprime.
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Cryptography
Cryptography or cryptology (from κρυπτός|translit.
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Degree of a polynomial
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
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Digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations.
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Digital waveguide synthesis
Digital waveguide synthesis is the synthesis of audio using a digital waveguide.
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Divided differences
In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions.
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Edward Waring
Edward Waring (15 August 1798) was a British mathematician.
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Finite difference coefficient
In mathematics, to approximate a derivative to an arbitrary order of accuracy, it is possible to use the finite difference.
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Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
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Finite impulse response
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time.
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Frobenius covariant
In matrix theory, the Frobenius covariants of a square matrix are special polynomials of it, namely projection matrices Ai associated with the eigenvalues and eigenvectors of.
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Horner's method
In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S..) is either of two things.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
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Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
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Lebesgue constant (interpolation)
In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomial approximation of the function (the degree of the polynomials are obviously fixed).
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Monomial basis
In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all monomials.
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Neville's algorithm
In mathematics, Neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician Eric Harold Neville.
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Newton polynomial
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points.
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Newton–Cotes formulas
In numerical analysis, the Newton–Cotes formulae, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulae for numerical integration (also called quadrature) based on evaluating the integrand at equally spaced points.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.
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Philosophical Transactions of the Royal Society
Philosophical Transactions, titled Philosophical Transactions of the Royal Society (often abbreviated as Phil. Trans.) from 1776, is a scientific journal published by the Royal Society.
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Physical modelling synthesis
Physical modelling synthesis refers to sound synthesis methods in which the waveform of the sound to be generated is computed using a mathematical model, a set of equations and algorithms to simulate a physical source of sound, usually a musical instrument.
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Polynomial interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset.
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Runge's phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.
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Shamir's Secret Sharing
Shamir's Secret Sharing is an algorithm in cryptography created by Adi Shamir.
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Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.
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Sylvester's formula
In matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function of a matrix as a polynomial in, in terms of the eigenvalues and eigenvectors of.
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Table of Newtonian series
In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence a_n written in the form where is the binomial coefficient and (s)_n is the rising factorial.
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Vandermonde matrix
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m × n matrix 1 & \alpha_1 & \alpha_1^2 & \dots & \alpha_1^\\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_2^\\ 1 & \alpha_3 & \alpha_3^2 & \dots & \alpha_3^\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & \alpha_m & \alpha_m^2 & \dots & \alpha_m^ \end, or for all indices i and j. (Some authors use the transpose of the above matrix.) The determinant of a square Vandermonde matrix (where m.
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Barycentric Interpolation, Lagrange form, Lagrange interpolant, Lagrange interpolating polynomial, Lagrange interpolation, Lagrange interpolation formula, Lagrange interpolation polynomial, Lagrange polynomials, Lagrangian Interpolation, Lagrangian interpolation.
References
[1] https://en.wikipedia.org/wiki/Lagrange_polynomial
