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}
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41A05
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41A10Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}
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41A15Spline approximation
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41A17Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
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41A20Approximation by rational functions
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41A21Padé approximation
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41A25Rate of convergence, degree of approximation
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41A27Inverse theorems
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41A28Simultaneous approximation
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41A29Approximation with constraints
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41A30Approximation by other special function classes
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41A35Approximation by operators (in particular, by integral operators)
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41A36Approximation by positive operators
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41A40Saturation
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41A44Best constants
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41A45Approximation by arbitrary linear expressions
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41A46Approximation by arbitrary nonlinear expressions; widths and entropy
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41A50Best approximation, Chebyshev systems
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41A52Uniqueness of best approximation
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41A55Approximate quadratures
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41A58Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
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41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
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41A63Multidimensional problems (should also be assigned at least one other classification number in this section)
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41A65Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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41A80Remainders in approximation formulas
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41A99None of the above, but in this section