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Exact Solution of a Linear Difference Equation in a Finite Number of Steps
Department of Management, ‘VNIIEM Corporation’ JC, Moscow, Russia
Department of Ship Electricity and Automatics, Northern (Arctic) Federal University, Severodvinsk, Russia
- 1 Department of Management, ‘VNIIEM Corporation’ JC, Moscow, Russia
- 2 Department of Ship Electricity and Automatics, Northern (Arctic) Federal University, Severodvinsk, Russia
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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.
KeywordsLinear Difference EquationExact Iterative Solution of a System of Linear Algebraic EquationsNilpotent Matrix
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