Estimates of Solutions to Infinite Systems of Linear Equations and the Problem of Interpolation by Cubic Splines on the Real Line

We study the solvability of bi-infinite systems of linear equations whose matrices are diagonally dominant. We prove that the estimates of the norm of the solution in terms of the diagonal dominance value well-known in the case of finite systems of linear equations are also valid for bi-infinite sys...

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Bibliographic Details
Published in:Siberian mathematical journal 2022-07, Vol.63 (4), p.677-690
Main Authors: Volkov, Yu. S., Novikov, S. I.
Format: Article
Language:English
Subjects:
Estimates
Interpolation
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
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Summary:We study the solvability of bi-infinite systems of linear equations whose matrices are diagonally dominant. We prove that the estimates of the norm of the solution in terms of the diagonal dominance value well-known in the case of finite systems of linear equations are also valid for bi-infinite systems of equations. The estimates are used in interpolation by splines on nonuniform meshes on the real line. Using the estimates, we prove the existence and uniqueness of a cubic spline of linear or quadratic growth interpolating data of linear or quadratic growth, without any constraints on node spacing. The familiar estimates of the interpolation error on a segment are carried over to the case of interpolation on the whole real line.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622040085