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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]
• 18
  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