Symbolic Algorithm for Solving SLAEs with Multi-Diagonal Coefficient Matrices
Milena Veneva
TL;DR
This paper introduces a symbolic algorithm for efficiently solving systems of linear equations with multi-diagonal matrices, including correctness proof and complexity analysis.
Contribution
It provides a generalized symbolic algorithm with proven correctness conditions and complexity estimation for multi-diagonal linear systems.
Findings
Algorithm is correct under specified conditions.
Complexity formula for the symbolic algorithm is derived.
The approach generalizes existing methods for multi-diagonal systems.
Abstract
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 multi-diagonal numerical algorithm is obtained.
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