Description

Jacobi, Gauss-Siedel and relaxation iterative methods for solving linear systems
Consider the system Ax = b; with A = (aij)i;j=1 ;n, x = (x1;:::; xn)0 and b = (b1;:::; bn)0:
Input: A -matrix of coe¢ cients; b -vector of free terms; x(0) -the initial approximation of the solution; ” -precision, N – maximum number of iterations; (! parameter for relaxation method);
Output: x -vector of the solutions or a message – in case that the maximum number of iterations is exceeded.
Problem:
1. Solve the following system using Jacobi, Gauss-Seidel and relaxation iterative methods, for ” = 10 3 :
:
Return the solution of the system and the number of iterations needed for nding the solution.
2. Solve the following system using the matriceal forms of Jacobi, GaussSeidel and relaxation methods, for ” = 10 5 :
:
1