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Approximation theory: Quiz

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Question 1: One can obtain polynomials very close to the optimal one by expanding the given function in terms of ________ and then cutting off the expansion at the desired degree.
Legendre polynomialsOrthogonal polynomialsHypergeometric seriesChebyshev polynomials

Question 2: This is typically done with ________ or rational (ratio of polynomials) approximations.
PolynomialPrime numberField (mathematics)Algebra

Question 3: One problem of particular interest is that of approximating a function in a ________ mathematical library, using operations that can be performed on the computer or calculator (e.g.
Central processing unitLinuxPersonal computerComputer

Question 4: Chebyshev approximation is the basis for Clenshaw–Curtis quadrature, a ________ technique.
IntegralNumerical analysisMonte Carlo methodNumerical integration

Question 5: 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 ________ arithmetic.
Arbitrary-precision arithmeticFloating pointFixed-point arithmeticPrimitive data type

Question 6: This function changes sign at least N+1 times so, by the ________, it has N+1 zeroes, which is impossible for a polynomial of degree N.
Connected spaceIntermediate value theoremReal numberContinuous function

Question 7: 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 ________.
OrthogonalityHilbert spaceVector spaceOrthogonal polynomials

Question 8: In ________, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
GeometryMathematicsMathematical logicSet theory







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