TITLE:
Exact Solution of a Linear Difference Equation in a Finite Number of Steps
AUTHORS:
Albert Iskhakov, Sergey Skovpen
KEYWORDS:
Linear Difference Equation, Exact Iterative Solution of a System of Linear Algebraic Equations, Nilpotent Matrix
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.3,
March
29,
2018
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.