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
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 11, pp. 1691-1706
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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.
@article{ZVMMF_2014_54_11_a0,
author = {V. I. Gel'fgat},
title = {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},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1691--1706},
publisher = {mathdoc},
volume = {54},
number = {11},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a0/}
}
TY - JOUR AU - V. I. Gel'fgat TI - 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 JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2014 SP - 1691 EP - 1706 VL - 54 IS - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a0/ LA - ru ID - ZVMMF_2014_54_11_a0 ER -
%0 Journal Article %A V. I. Gel'fgat %T 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 %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2014 %P 1691-1706 %V 54 %N 11 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a0/ %G ru %F ZVMMF_2014_54_11_a0
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. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 11, pp. 1691-1706. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a0/