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1: 3.11 Approximation Techniques
§3.11(v) Least Squares Approximations
For further information on least squares approximations, including examples, see Gautschi (1997a, Chapter 2) and Björck (1996, Chapters 1 and 2). …
2: Bibliography P
  • M. J. D. Powell (1967) On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria. Comput. J. 9 (4), pp. 404–407.
  • 3: Bibliography B
  • Å. Björck (1996) Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • 4: 28.6 Expansions for Small q
    It is conjectured that for large n , the radii increase in proportion to the square of the eigenvalue number n ; see Meixner et al. (1980, §2.4). …
    28.6.20 lim inf n ρ n ( j ) n 2 k k ( K ( k ) ) 2 = 2.04183 4 ,
    5: 26.18 Counting Techniques
    With the notation of §26.15, the number of placements of n nonattacking rooks on an n × n chessboard that avoid the squares in a specified subset B is … The number of ways of placing n labeled objects into k labeled boxes so that at least one object is in each box is …
    6: Guide to Searching the DLMF
    Table 1: Query Examples
    Query

    Matching records contain

    Fourier or series

    at least one of the words “Fourier” or “series”.

    Fourier (transform or series)

    at least one of “Fourier transform” or “Fourier series”.

    J_n@(x or z)=

    at least one of the math fragments J n ( x ) = or J n ( z ) , emphasizing that J n is a function.

    sin x and (J_nu(z) or I_nu(z))

    both sin x and at least one of the two functions J ν ( z ) or I ν ( z ) .

    trigonometric^2 + trig$^2

    any sum of the squares of two trigonometric functions such as sin 2 z + cos 2 z .

    7: 1.4 Calculus of One Variable
    Square-Integrable Functions
    A function f ( x ) is square-integrable if …
    1.4.33 𝒱 a , b ( f ) = sup j = 1 n | f ( x j ) - f ( x j - 1 ) | ,