The Right, Left and Counter Transposition fro the Solution of the System of Linear Algebraic Equations with Five-diagonal, Cyclic Matrixes
by
Hrant Hovhannissian

The fourth series, linear, with changing coefficients, differential equation, at boundary conditions, while solving with a method of grids, is received five-diagonal, with cyclic-matrix linear algebraic system of equations. In research work is derived the algorithm for solving the proposed problem. Assume that

Ax = f (1)

the system of linear algebraic equations, where A is n ×n measuring unit with five-diagonal, cyclic matrix. (1) the solving of system we seek in this form:

x = u + x₁v + x_nw (2)

where u, w, v (n-2) measuring vectors, which are solved from the following linear algebraic system of equations:

Bu = f1 (3)
Bv = f2 (4)
Bw = f3 (5)

where B is (n-2) ×(n-2) five-diagonal matrix. (3), (4) and (5) linear algebraic system of equations is solved with the help of right, left and counter transposition method. After which for x₁ and x_n the unknown values are received 2 ×2 measuring units with linear algebraic system of equation which solved with the method of Kramer.

Having u, v, w vectors, x₁ and x_n values, with the help of (2) equation is solved the solutions of equations.

Date received: January 27, 2000