Approximation Theory
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Home > Art, Film & Photography > Approximation Theory: Euler-Maclaurin Formula, Chebyshev Polynomials, Modulus of Continuity, Approximation Theory, Remez Algorithm
Approximation Theory: Euler-Maclaurin Formula, Chebyshev Polynomials, Modulus of Continuity, Approximation Theory, Remez Algorithm

Approximation Theory: Euler-Maclaurin Formula, Chebyshev Polynomials, Modulus of Continuity, Approximation Theory, Remez Algorithm


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Euler-maclaurin Formula, Chebyshev Polynomials, Modulus of Continuity, Approximation Theory, Remez Algorithm, Szsz-mirakyan Operator, Hilbert Matrix, Dirichlet Kernel, Trigonometric Polynomial, Unisolvent Functions, Baskakov Operator, Favard Operator, Jackson's Inequality, Szsz-mirakjan-kantorovich Operator, Lebesgue's Lemma, Universal Differential Equation. Excerpt: 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 what is meant by best and simpler will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials . One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational (ratio of polynomials) approximations. The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing the domain can often be done through the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment. Error between o...


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Product Details
  • ISBN-13: 9781155657578
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 70
  • Spine Width: 4 mm
  • Weight: 113 gr
  • ISBN-10: 1155657578
  • Publisher Date: 06 May 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Euler-Maclaurin Formula, Chebyshev Polynomials, Modulus of Continuity, Approximation Theory, Remez Algorithm
  • Width: 229 mm


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