Mathematical Sciences Classification System

41Axx - Approximations and expansions
{For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx}

  • 15
    41A05
    Interpolation [See also 42A15 and 65D05]
  • 16
    41A10
    Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}
  • 11
    41A15
    Spline approximation
  • 5
    41A17
    Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
  • 4
    41A20
    Approximation by rational functions
  • 7
    41A21
    Padé approximation
  • 10
    41A25
    Rate of convergence, degree of approximation
  • 41A27
    Inverse theorems
  • 1
    41A28
    Simultaneous approximation
  • 41A29
    Approximation with constraints
  • 12
    41A30
    Approximation by other special function classes
  • 5
    41A35
    Approximation by operators (in particular, by integral operators)
  • 6
    41A36
    Approximation by positive operators
  • 1
    41A40
    Saturation
  • 1
    41A44
    Best constants
  • 1
    41A45
    Approximation by arbitrary linear expressions
  • 2
    41A46
    Approximation by arbitrary nonlinear expressions; widths and entropy
  • 5
    41A50
    Best approximation, Chebyshev systems
  • 41A52
    Uniqueness of best approximation
  • 2
    41A55
    Approximate quadratures
  • 4
    41A58
    Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
  • 12
    41A60
    Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
  • 14
    41A63
    Multidimensional problems (should also be assigned at least one other classification number in this section)
  • 13
    41A65
    Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
  • 1
    41A80
    Remainders in approximation formulas
  • 41A99
    None of the above, but in this section

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