Abstract:
In this paper, we consider an algorithm that allows you to calculate the sequence of the main minors of the Toeplit.z band matrix associated with the Cauchy problem for a two-dimensional polynomial difference operator with constant coefficients, with an upper (lower) band width equal to one, which allows us to determine the non-degeneracy of such a matrix and, therefore, draw conclusions on the solvability of the Cauchy problem.
Keywords:
polynomial difference operator, Cauchy problem, solvability, band matrix, toeplit.z matrix, main minor.
Funding agency
The work f the first author is supported by the Russian Federal Property Fund in the framework of scientific project textnumero 18-31-00232.
Received: 18.03.2020
Document Type:
Article
UDC:
517.55-519.85-519.111.1
Language: Russian
Linking options:
https://www.mathnet.ru/eng/pmf56
This publication is cited in the following 1 articles:
M. S. APANOVICH, A. P. LYAPIN, K. V. SHADRIN, “SOLVING THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL DIFFERENCE EQUATION IN A PARALLELEPIPED”, Programmirovanie, 2023, no. 2, 5
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