##### La Classification MathÃ©matique par matiÃ¨res 2000Mathematics subject Classification 2000
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41-XX Approximations and expansions [For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx]

• 41-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 41-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 41-02 Research exposition (monographs, survey articles)
• 41-03 Historical (must also be assigned at least one classification number from Section 01)
• 41-04 Explicit machine computation and programs (not the theory of computation or programming)
• 41-06 Proceedings, conferences, collections, etc.
• 41-99 Approximations and expansions (not classified at a more specific level)
• 41A10 Approximation by polynomials [For approximation by trigonometric polynomials, see 42A10]
• 41A15 Spline approximation
• 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol'skij-type inequalities)
• 41A20 Approximation by rational functions
• 41A25 Rate of convergence, degree of approximation
• 41A27 Inverse theorems
• 41A28 Simultaneous approximation
• 41A29 Approximation with constraints
• 41A30 Approximation by other special function classes
• 41A35 Approximation by operators (in particular, by integral operators)
• 41A36 Approximation by positive operators
• 41A40 Saturation
• 41A44 Best constants
• 41A45 Approximation by arbitrary linear expressions
• 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
• 41A50 Best approximation, Chebyshev systems
• 41A52 Uniqueness of best approximation