Title of article :
Symbolic computation of the Duggal transform
Author/Authors :
Pappas, D. Department of Statistics - University of Economics and Business, Athens, Greece , Katsikis, V. N. Department of Economics - Division of Mathematics and Informatics - University of Athens Athens, Greece , Stanimirovic, I. P. Department of Computer Science - Faculty of Science and Mathematics - University of Nis, Serbia
Abstract :
Following the results of [6], regarding the Aluthge transform of polynomial ma-
trices, the symbolic computation of the Duggal transform of a polynomial matrix A is de- veloped in this paper, using the polar decomposition and the singular value decomposition of A. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical characteristics. The introduced algorithm is proven and illustrated in numerical examples. We also represent symbolically the Duggal transform of rank-one matrices using cross products of vectors and show that the Duggal transform of such matrices can be given explicitly by a closed formula and is equal to its Aluthge transform. c
Keywords :
Duggal transform , symbolic computation , polar decomposition , PSVD algorithm , polynomial matrices , rank 1 matrices
Journal title :
Astroparticle Physics
