To get better values, the approximations in previous iterations are used. In Gauss Jacobi method, we assume x1, x2 and x3 as the three initial guesses.

Whether it’s a program, algorithm, or flowchart, we start with a guess solution of the given system of linear simultaneous equations, and iterate the equations till the desired degree of accuracy is reached. Both are based on fixed point iteration method. Gauss-Seidel and Gauss Jacobi method are iterative methods used to find the solution of a system of linear simultaneous equations. norm ( res, 2 ) < tol ) : print ( 'Converged after ', iter, 'iterations' ) return x #start of Jacobi iteration for i in range ( n ) : sum = 0.0 for j in range ( n ) : if ( i != j ) : sum += A * x x = ( f - sum ) / A print ( 'Failed to converge after ', iter, 'iterations' ) return x A = numpy. flatten ( ) #check L2-norm of the residual for convergence if ( nl. shape != n ) : print ( 'Error! Incompatible array and vector sizes.' ) return f #Set up a loop to iterate until we converge to a solution or we reach the max number of iterations for iter in range ( maxIter ) : #calculate residual res = f - numpy. size #Begin bychecking for compatiable matrix and rhs sizes if ( A.

linalg as nl def gaussSeidel ( A, f, x, maxIter = 100, tol = 1.0e-4 ) : #inputs: #A is a nXn matrix #f is is a right-hand-side vector of length n #x is initial guess at the solution to Ax = f #maxIter (optional) is max number of Jacobi iterations #tol (optional) is the desired accuracy in terms of the L2-norm of the residual (f-Ax) n = f. array ( ) sol = jacobi ( A, f, x ) print ( sol ) copy ( xnew ) print ( 'Failed to converge after ', iter, 'iterations' ) return x A = numpy. norm ( res, 2 ) < tol ) : print ( 'Converged after ', iter, 'iterations' ) return x #start of Jacobi iteration for i in range ( n ) : sum = 0.0 for j in range ( n ) : if ( i != j ) : sum += A * x xnew = ( f - sum ) / A x = numpy. dot ( A, x ) #check L2-norm of the residual for convergence if ( nl. copy ( x ) for iter in range ( maxIter ) : #calculate residual res = f - numpy. shape != n ) : print ( 'Error! Incompatible array and vector sizes.' ) return f #Set up a loop to iterate until we converge to a solution or we reach the max number of iterations xnew = numpy.

linalg as nl def jacobi ( A, f, x, maxIter = 100, tol = 1.0e-4 ) : #inputs: #A is a nXn matrix #f is is a right-hand-side vector of length n #x is initial guess at the solution to Ax = f #maxIter (optional) is max number of Jacobi iterations #tol (optional) is the desired accuracy in terms of the L2-norm of the residual (f-Ax) n = f.

Python gauss seidel