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Solve the following using the Gauss-Seidel Method. [A] = [4 -2 1; 1 5 -3; 2 2 5]

ID: 3631616 • Letter: S

Question

Solve the following using the Gauss-Seidel Method.


[A] = [4 -2 1; 1 5 -3; 2 2 5]
{b} = {11;-6;7}


Please show your code.

Thanks

Explanation / Answer

coeff = [4 -2 1; 1 5 -3; 2 2 5]; constants = [11;-6;7]; tol = 0.001; n = length(constants); checktol = ones(n,1);%Used for Error term evaluation X = zeros(n,1); %Gauss-Siedel iterations iteration = 0; while max(checktol) > tol iteration = iteration + 1; Z = X; for i = 1:n j = 1:n; j(i) = []; Xtemp = X; Xtemp(i) = []; X(i) = (constants(i) - sum(coeff(i,j) * Xtemp)) / coeff(i,i); end Xsolution(:,iteration) = X; checktol = sqrt((X - Z).^2);%Recalculating the error term end solution = [X] ++++++++++++++++++++++++++++++++++++++++ A nice explanation on Gauss-siedel method using Matlab available from here. You can give a try. It's good article. https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/04LinearAlgebra/gauss/

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