Symbolic algorithm for solving SLAEs with multi-diagonal coefficient matrices

Systems of linear algebraic equations with multi-diagonal coefficient matrices may arise after many different scientific and engineering problems, as well as problems of the computational linear algebra where finding the solution of such a system of linear algebraic equations is considered to be one...

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Vydané v:Discrete and continuous models and applied computational science Ročník 33; číslo 1; s. 46 - 56
Hlavný autor: Milena, Veneva
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Peoples’ Friendship University of Russia (RUDN University) 15.06.2025
Predmet:
complexity of numerical algorithms
computational methods for sparse matrices
numerical analysis
numerical mathematical programming methods
ISSN:2658-4670, 2658-7149
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Abstract Systems of linear algebraic equations with multi-diagonal coefficient matrices may arise after many different scientific and engineering problems, as well as problems of the computational linear algebra where finding the solution of such a system of linear algebraic equations is considered to be one of the most important problems. This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of the algorithm is formulated and proven. Formula for the complexity of the multidiagonal numerical algorithm is obtained.
AbstractList Systems of linear algebraic equations with multi-diagonal coefficient matrices may arise after many different scientific and engineering problems, as well as problems of the computational linear algebra where finding the solution of such a system of linear algebraic equations is considered to be one of the most important problems. This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of the algorithm is formulated and proven. Formula for the complexity of the multidiagonal numerical algorithm is obtained.
Author Milena, Veneva
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Cites_doi 10.1007/978-3-319-97277-0_33
10.1137/1.9780898718027
10.1007/s11075-012-9626-2
10.1051/epjconf/201817707004
10.1051/epjconf/201921405004
10.26456/mmg/2018-633
10.1155/2015/232456
10.4236/am.2012.34052
10.1007/978-3-0348-9272-8
10.1093/oso/9780198502388.001.0001
10.4236/ajcm.2015.53023
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SubjectTerms complexity of numerical algorithms
computational methods for sparse matrices
numerical analysis
numerical mathematical programming methods
Title Symbolic algorithm for solving SLAEs with multi-diagonal coefficient matrices
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