41XX 


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} 

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} 


41A05 
Interpolation [See also 42A15 and 65D05] 


41A10 
Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10} 


41A15 
Spline approximation 


41A17 
Inequalities in approximation (Bernstein, Jackson, Nikolʹskiĭtype inequalities) 


41A20 
Approximation by rational functions 


41A21 
Padé approximation 


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 


41A55 
Approximate quadratures 


41A58 
Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 


41A60 
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 


41A63 
Multidimensional problems (should also be assigned at least one other classification number in this section) 


41A65 
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 


41A80 
Remainders in approximation formulas 


41A99 
None of the above, but in this section 