Geodesic
On the principal and strictly particular solutions to infinite systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 351-362

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The concepts of the principal solution to infinite systems of linear algebraic equations and the reduction method are defined more precisely. The principal solution, if it exists, is a strictly particular solution to the infinite system. If the reduction method is convergent, then it necessarily converges to Kramer’s determinant; however, Kramer’s determinant is not always a solution to the infinite system. To confirm the obtained results, analytical and numerical solutions of specific infinite system are considered. 
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O. F. Ivanova; N. N. Pavlov; F. M. Fedorov. On the principal and strictly particular solutions to infinite systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 351-362. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a1/