Exact Solution of a Linear Difference Equation in a Finite Number of Steps

Sergey Mikhailovich Skovpen; Albert Saitovich Iskhakov

doi:10.24297/jam.v14i1.7206

Authors

Sergey Mikhailovich Skovpen Northern (Arctic) Federal University
Albert Saitovich Iskhakov 'VNIIEM Corporation' JC

DOI:

https://doi.org/10.24297/jam.v14i1.7206

Keywords:

Nilpotent Matrix, Linear Difference Equation, Exact Iterative Solution of a System of Linear Algebraic Equations

Abstract

An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

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References

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