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Jacobi method: Error with index in the while loop.

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Luis Garcia
Luis Garcia 2018-3-2
编辑： Jan 2018-3-2
N = 6;
I = eye(N);
A = toeplitz([2 -1 zeros(1, N-2)]);
b = [0 2 3 -1 2 1]';
x = [0 0 0 0 0 0]'; %initial guess
diagonal = diag(diag(A));
upper = triu(A);
lower = tril(A);
normValue = Inf;
B_jacobi = -inv(diagonal)*(lower+upper);
c_jacobi = inv(diagonal)*b;
eigen_value_jacobi = eig(B_jacobi);
B_gs = -inv(I+(inv(diagonal)*lower))*(inv(diagonal)*upper);
c_gs = inv(I+(inv(diagonal*lower)))*(inv(diagonal)*b);
eigen_value_gs = eig(B_gs);
%disp(A);
%Jacobi method
k = 1;
Tol = 0.001;
while normValue > Tol
x(k) = B_jacobi*x(k-1) + c_jacboi;
k= k+1;
normValue= norm(x(k) - x(k-1));
end

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回答（1 个）

Jan
Jan 2018-3-2
编辑：Jan 2018-3-2
This cannot work:
k = 1;
while normValue > Tol
x(k) = B_jacobi*x(k-1) + c_jacboi;
because in the 1st iteration k=1 you try to evaluate x(k-1), but k-1 is 0.
Simply start with k = 2.
Then replace "c_jacboi" by "c_jacobi".
Now you have the problem, that
B_jacobi*x(k-1) + c_jacobi
replies a matrix, but you try to assign it to the scalar x(k).
Maybe you want:
while normValue > Tol
xNew = B_jacobi*x + c_jacboi;
k = k+1;
normValue = norm(x - xNew);
x = xNew;
end
Please read the documentation of inv:
doc inv
There you find the important hint, that the slash operator is much better.
B_jacobi = -diagonal \ (lower + upper);

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