Iterative Method for Solution of Simultaneous Linear Equation
All the previous methods seen in solving the system of simultaneous algebraic linear equations are direct methods. Now we will see some indirect methods or iterative methods.
This iterative methods is not always successful to all systems of equations. If this method is to succeed, each equation of the system must possess one large coefficient and the large coefficient must be attached to a different unknown in that equation. This condition will be satisfied if the large coefficients are along the leading diagonal of the coefficient matrix. When this condition is satisfied, the system will be solvable by the iterative method. The system,
will be solvable by this method if
In other words, the solution will exist (iterating will converge) if the absolute values of the leading diagonal elements of the coefficient matrix A of the system AX = B are greater than the sum of absolute values of the other coefficients of that row. The condition is sufficient but not necessary.
Under the category of iterative method, we shall describe the following two methods:
(i) Jacobi’s method (ii) Gauss-Seidel method.
Переглядів: 172
Не знайшли потрібну інформацію? Скористайтесь пошуком google: