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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 11, Pages 1691–1706
DOI: https://doi.org/10.7868/S0044466914110052 (Mi zvmmf10105) 		 
Matrices of small Toeplitz rank, certain representations of the solution to an unstable system of linear equations with Toeplitz coefficient matrices, and related fast algorithms for solving such systems

V. I. Gel'fgat

AKMA Nongovernmental Pension Fund, ul. Shvernika 4, Moscow, 117036, Russia
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DOI: https://doi.org/10.7868/S0044466914110052
Abstract: Formulas for inverting regularized systems of linear equations whose coefficient matrices are complex, Toeplitz, and singular or nearly singular are derived. They make it possible to develop economical algorithms for solving such systems in mass calculations.
Key words: matrices, Toeplitz matrices, matrix inversion, unstable systems of linear equations, regularization, circulants, skew-circulants, spectral decompositions, economical numerical algorithms.
Received: 15.04.2013
Revised: 13.02.2014
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 11, Pages 1627–1642
DOI: https://doi.org/10.1134/S0965542514110050
Bibliographic databases:
Document Type: Article
UDC: 519.614
Language: Russian
Citation: V. I. Gel'fgat, “Matrices of small Toeplitz rank, certain representations of the solution to an unstable system of linear equations with Toeplitz coefficient matrices, and related fast algorithms for solving such systems”, Zh. Vychisl. Mat. Mat. Fiz., 54:11 (2014), 1691–1706; Comput. Math. Math. Phys., 54:11 (2014), 1627–1642
Citation in format AMSBIB
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