Estimates for solutions of bi-infinite systems of linear equations

We consider the problem of estimating in uniform norm solutions of nonhomogeneous difference equations. Difference equations are considered as bi-infinite systems of linear algebraic equations. We give the estimate for Laurent’s matrices with diagonal dominance. Based on this result and an idea of d...

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Bibliographic Details
Published in:European journal of mathematics 2022, Vol.8 (2), p.722-731
Main Authors: Volkov, Yuriy S., Novikov, Sergey I.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Difference equations
Estimates
Linear algebra
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
Research Article
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Summary:We consider the problem of estimating in uniform norm solutions of nonhomogeneous difference equations. Difference equations are considered as bi-infinite systems of linear algebraic equations. We give the estimate for Laurent’s matrices with diagonal dominance. Based on this result and an idea of decomposition of the matrix into a product of matrices associated with factorization of the characteristic polynomial, we propose estimates for any nonsingular banded Laurent matrix. The established estimates are attainable.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-021-00528-y