then the value of x becomes a smaller negative value to compensateĪfter some time, you get infinities and NaNs.

then x*a + x*a is negative, and the value of x becomes larger to compensate,.

Thus x gets an even smaller negative value than in the first round,

the sum x*a + x*a is positive, since both x and a are negative, and x and a are positive.

then, to compensate for the too large value of x, x gets a negative value too.

next, the sum for the second row becomes negative, and x gets a too large value,.

If you reorder the equations, move the first equation last (then the coefficient matrix becomes diagonally dominant), it quickly converges to the approximate solution x=0.500006 Your example matrix isn't, so it mustn't come as a too big surprise that the method doesn't converge. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either diagonally dominant, or symmetric and positive definite.Īs it is stated in the wikipedia article. Current solution: 0.99994242 2.00008477 -1.00006833 1. Define a function jacobi (A, b, x, eps, maxn), where A is the matrix A, b is the vector b, x is the initial guess of the solution, eps is the This problem has been solved You'll get a detailed solution from a subject matter expert that helps you learn core concepts. The minimum amount of storage is two vectors of size n. Printf('Enter the co-efficients of the equations: ') Unlike the GaussSeidel method, we cant overwrite xi ( k ) with xi ( k +1), as that value will be needed by the rest of the computation. Printf('Enter the number of equations: ') When I am running with this input,there is a run time error of 'floating point overflow.'It is working fine if I am using integer input.My code is as follows: What mistakes did I make? I think it is in TriSolve method since if I replaced it with regular LU solver such as (np.linalg.solve) it works.I have done the programming for gauss-seidel method,which is working for all inputs,except the following equation: 1.876 x1+2.985 x2-11.620 x3=-0.972

cpp parallel-computing comparison numerical-methods jacobi matrix-calculations seidel gauss-seidel parallel-programming openmp-parallelization gauss-jacobi felipe-gimenez. Below is the same implementation in MATLAB which works: function x = gSeidel(A,B,N) Algorithm to compare numerical methods (Gauss Jacobi and Gauss Seidel), using implementation sequential and parallel ( C++ and OpenMP ). For some reason it is not converging even after 50000 iterations to the solution even when the matrix A is strict diagonal dominant. #O(n) per iteration, so overall O(nN), good for large SPD/SDD matricesĪ = np.array(,])Īns = is my Gauss-Seidel method in Python.

From scipy.linalg import solve_triangular as triSolve

Python code for gauss seidel method