A Simple Iterative Method for Exact Solution of Systems of Linear Algebraic Equations
Albert Iskhakov1, Sergey Skovpen2
Citation : Albert Iskhakov, Sergey Skovpen, A Simple Iterative Method for Exact Solution of Systems of Linear Algebraic Equations International Journal of Scientific and Innovative Mathematical Research 2019 , 7(2) : 33-34
We present for the first time a theorem (with proof) of solving a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix. The system is transformed such that the spectrum of the matrix to be unit. Splitting the matrix gives a nilpotent matrix of the iteration system that generates an exact solution of SLAE for a number of iterations not exceeding the dimension of the system.