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 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.