Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Fast Lagrange--Newton transformations
Journal of Complexity
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In this paper we present explicit formulae for the multivariate Lagrange-Newton transformation T:K^n^"^1^x^n^"^2^x^...^x^n^"^d-K^n^"^1^x^n^"^2^x^...^x^n^"^d and its inverse T^-^1 with respect to points x"i","j=@l"ix"i","j"-"1+@d"i (i=1,2,...,d,j=1,2,...,n"i-1), where @l"i0, @d"i and x"i","0=@k"i belong to the field K. Moreover, we derive fast algorithms for computing these transformations. The running time of them is O(@?"j"="1^dn"j@?log@?"j"="1^dn"j)+O(d@?"j"="1^dn"j) base operations from K.