Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangement invariant sets of derivatives

1987 ◽  
Vol 13 (4) ◽  
pp. 281-306 ◽  
Author(s):  
V. F. Babenko
Keyword(s):  
Invariant Sets ◽  
Periodic Functions ◽  
Quadrature Formulae ◽  
Optimal Quadrature ◽  
Optimal Quadrature Formulae

scholarly journals Optimal quadrature formulae and minimal monosplines in Lq

1970 ◽  
Vol 11 (1) ◽  
pp. 48-56 ◽  
Author(s):  
J. Kautsky
Keyword(s):  
Quadrature Formula ◽  
Quadrature Formulae ◽  
Optimal Quadrature ◽  
Derivatives Of ◽  
Optimal Quadrature Formulae ◽  
Optimal Formula

SummaryThe quadrature formula of order m using values of derivatives up to the m — 1st order with the best possible bound in is derived. Using certain properties of the polynomials minimal in Lq norm, it is proved that the optimal formula not use the derivatives of m — 1st order if m is even.

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