CONVERGENCE OF EXPANSIONS INTO CONTINUED FRACTIONS OF SOLUTIONS OF MATRIX POLYNOMIAL EQUATIONS
Keywords:
матричні рівняння, критерії збіжності наближених методів до розв’язку, періодичні матричні ланцюгові дроби.Abstract
In this work, an approach for matrix equations is proposed, which allows to significantly clarify the conditions under which computational schemes will converge. The transformation for one-periodic matrix branched continued fractions into matrix continued fractions with block elements is obtained. This gives new sufficient signs of convergence to the solution of iterative methods for polynomial matrix equations of the nth order.
References
Bodnar D.I. Vetvyashchiyesya tsepnyye drobi. - K.: Naukova dumka, 1986. - 176 s.
Kh.D.Ikramov. Chislennoye resheniye matrichnykh uravneniy. - M: Nauka, 1984. - 192 s.
Nedashkovskyy M.O. Oznaky zbizhnosti matrychnykh hillyastykh lanzhuyovykh drobiv. Matematychni metody ta fizyko-mekhanichni polya. Lviv, 2003, tom 46, №4, s.50-56.
Dorożyński, J., Nedashkovskyy, M. Computer methods for calculating tuple solutions of polynomial matrix equations, 2020 Bulletin of the Polish Academy of Sciences: Technical Sciences 68(2), pp. 235-243.
L.Lorentzen, H.Waadeland. Continued fractions with applications. Amsterdam: Elsevier Publishers B.V.,1992 - 606 p.
Wall H.S. – Analytic theory of continued fractions. - N. Y., 1948, 433 p.
