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On Simultaneous Optimization of Norms of Derivatives of Lagrange Interpolation Polynomials
Author(s) -
Szabados J.,
Vértesi P.
Publication year - 1989
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/21.5.475
Subject(s) - mathematics , lagrange polynomial , interpolation (computer graphics) , norm (philosophy) , trigonometric interpolation , polynomial interpolation , order (exchange) , birkhoff interpolation , derivative (finance) , second derivative , pure mathematics , algebra over a field , mathematical analysis , combinatorics , linear interpolation , polynomial , computer science , animation , computer graphics (images) , finance , political science , financial economics , law , economics
It is proved that the norm‖ ∑ k = 1 n( 1 − x k 2 )1 2 r| l k ( r )( x ) | ‖of the r th derivative of Lagrange interpolation polynomials can be of optimal order of magnitude only for three consecutive values of r .