Category: Approximation theory

Baskakov operator
In functional analysis, a branch of mathematics, the Baskakov operators are generalizations of Bernstein polynomials, Szász–Mirakyan operators, and . They are defined by where ( can be ), , and is a s
Discrete Chebyshev polynomials
In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by Pafnuty Chebyshev and rediscovered by Gra
Unisolvent functions
In mathematics, a set of n functions f1, f2, ..., fn is unisolvent (meaning "uniquely solvable") on a domain Ω if the vectors are linearly independent for any choice of n distinct points x1, x2 ... xn
Haar space
In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace of , where is a compact space and either the real numbers or the complex numbers, such that for any given ther
Zolotarev polynomials
In mathematics, Zolotarev polynomials are polynomials used in approximation theory. They are sometimes used as an alternative to the Chebyshev polynomials where accuracy of approximation near the orig
Hilbert matrix
In linear algebra, a Hilbert matrix, introduced by Hilbert, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded a
Lebesgue's lemma
For Lebesgue's lemma for open covers of compact spaces in topology see Lebesgue's number lemma In mathematics, Lebesgue's lemma is an important statement in approximation theory. It provides a bound f
Journal of Approximation Theory
The Journal of Approximation Theory is "devoted to advances in pure and applied approximation theory and related areas."
Chebyshev polynomials
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as and . They can be defined in several equivalent ways, one of which starts with trigonome
Favard operator
In functional analysis, a branch of mathematics, the Favard operators are defined by: where , . They are named after Jean Favard.
Whitney inequality
In mathematics, the Whitney inequality gives an upper bound for the error of best approximation of a function by polynomials in terms of the moduli of smoothness. It was first proved by Hassler Whitne
Constructive Approximation
Constructive Approximation is "an international mathematics journal dedicated to Approximations and Expansions and related research in computation, function theory, functional analysis, interpolation
Least-squares function approximation
In mathematics, least squares function approximation applies the principle of least squares to function approximation, by means of a weighted sum of other functions. The best approximation can be defi
Euler–Maclaurin formula
In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to eval
Radial basis function interpolation
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The
Unisolvent point set
In approximation theory, a finite collection of points is often called unisolvent for a space if any element is uniquely determined by its values on . is unisolvent for (polynomials in n variables of
Modulus of smoothness
In mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are used in approximation theory and numerica
Fekete problem
In mathematics, the Fekete problem is, given a natural number N and a real s ≥ 0, to find the points x1,...,xN on the 2-sphere for which the s-energy, defined by for s > 0 and by for s = 0, is minimal
Remez algorithm
The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations
Semi-infinite programming
In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a fin
Universal differential equation
A universal differential equation (UDE) is a non-trivial differential algebraic equation with the property that its solutions can approximate any continuous function on any interval of the real line t
Bernstein's theorem (polynomials)
Bernstein's theorem is an inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its derivative on the unit disk. It was proven by Sergei
Elliott Ward Cheney Jr.
Elliott Ward Cheney Jr. (June 28, 1929 – July 13, 2016) was an American mathematician and an emeritus professor at the University of Texas at Austin. Known to his friends and colleagues as Ward Cheney
Constructive function theory
In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximat
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that wh
Szász–Mirakjan–Kantorovich operator
In functional analysis, a discipline within mathematics, the Szász–Mirakjan–Kantorovich operators are defined by where and .
Szász–Mirakyan operator
In functional analysis, a discipline within mathematics, the Szász–Mirakyan operators (also spelled "Mirakjan" and "Mirakian") are generalizations of Bernstein polynomials to infinite intervals, intro
Jackson's inequality
In approximation theory, Jackson's inequality is an inequality bounding the value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity or mo
Dirichlet kernel
In mathematical analysis, the Dirichlet kernel, named after the German mathematician Peter Gustav Lejeune Dirichlet, is the collection of functions defined as where n is any nonnegative integer. The k
Modulus of continuity
In mathematical analysis, a modulus of continuity is a function ω : [0, ∞] → [0, ∞] used to measure quantitatively the uniform continuity of functions. So, a function f : I → R admits ω as a modulus o
Trigonometric polynomial
In the mathematical subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(nx) and cos(nx) with n taking on the values of
Bramble–Hilbert lemma
In mathematics, particularly numerical analysis, the Bramble–Hilbert lemma, named after James H. Bramble and Stephen Hilbert, bounds the error of an approximation of a function by a polynomial of orde