title: Proof of correctness of an algorithm that enhances the estimate of the rate of Seidel method convergence
metadata.name: dc.contributor.author
metadata.value: Borzykh, Alexey N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T16:12:11Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T16:12:11Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Borzykh A.N. Proof of correctness of an algorithm that enhances the estimate of the rate of Seidel method convergence. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 399–410.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.305
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16316
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article discusses the Seidel method for solving a system of linear algebraic equations x = Ax + f. It is a continuation of the previous paper by the author, where an algorithm for obtaining an estimate of the rate of Seidel method convergence was proposed. A more exhaustive proof of correctness of the algorithm is presented. The estimate given by this algorithm is better, than the estimate from the monograph “Computational methods of linear algebra” by Faddeev D.K., Faddeeva V.N. “Computational methods of linear algebra” although one needs an additional iterative process to obtain it. It is shown that this iterative process has at least linear rate of convergence, and its single step needs O(n) operations. The rate of convergence is estimated by the inequality |μ(Ak+1) − μ∗| < C|μ(Ak) − μ∗|, where C = 1− m5 12 , m is the smallest by absolute value element of matrix A, μ∗ is the limit value of the iterative process (the best estimate of the rate of Seidel method convergence), μ(Ak) and μ(Ak+1) are estimates obtained at k-th and (k + 1)-th steps of the iterative process, respectively.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Seidel method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: one-step cyclic process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: SLAE
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: system of linear algebraic equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: iterative solution methods
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Seidel method convergence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: estimate of the rate of Seidel method convergence
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Proof of correctness of an algorithm that enhances the estimate of the rate of Seidel method convergence
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 399-410.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16316/1/399-410.pdf
resources.format: Adobe PDF
resources.size: 314,33 kB