Abstract

EXTENSION OF RUTISHAUISER’S QU TRANSFORMATION METHOD TO THE COMPUTATION OF EIGENVALUES OF ARBITRARY RHOTRICES

Yakubu1,2*,D.Gulibur,Lohcwat2, Domven, Mathias1, L. Bernard and Bulus2,G. Lucy

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Abstract The purpose of this study is to extend Rutishauser’s procedure of computing eigenvalues of arbitrary matrices to the computation of eigenvalues of arbitrary rhotrices. The theory of rhotrix is a relatively new area of mathematical enrichment dealing with algebra and analysis of array of numbers in a mathematical rhomboidal form. A rhotrix can be transformed into matrix and vice versa, and the sizes of a rhotrix are always of odd dimensions. The procedure considers shift of origin in order to accelerate the convergence, thus leading to a greater effectiveness of the Rutishauser’s method. Numerical experiments show that the new transformation algorithm performs very well and faster, which demonstrate practically the effectiveness of the proposed method compared to some existing methods. Key words: Coupled matrix,Eigenvalues, LR algorithm, QR algorithm, qd algorithm

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