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33 lines
693 B
Matlab
33 lines
693 B
Matlab
function [x, errors] = JacobiMethod(A, b)
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%JACOBIMETHOD solves a system Ax = b using the Jacobi iterative method
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% The accuracy target is 10e-10
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% returns x - the solution and errors - vector of errors for each
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% iteration
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[L, D, U] = decomposeLDU(A);
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%Checking covergence conditions
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if ~(rowDominant(A) || columnDominant(A))
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sr = max(abs(eig(-inv(D)*(L+U))));
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if sr >= 1
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x = sr;
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return
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end
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end
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%Initial guess
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x = zeros(length(A), 1);
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Di = inv(D);
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iteration = 1;
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errors(iteration) = vecnorm(A*x - b);
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while errors(iteration) > 10^-10
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x = -Di * (L+U) * x + Di*b;
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iteration = iteration + 1;
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errors(iteration) = vecnorm(A*x - b);
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end
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