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System of equations with sparse linear equations

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Ghady Hajj
Ghady Hajj 2018-10-29
评论： Ghady Hajj 2018-10-30
Hello,
I have a sparse matrix A of size 65000x65000 only having 2's on the diagonal and 1's above and below the diagonal and the rest are zeros, and a system of equations in the form of X = A*B. The problem is that A is already a large matrix and MATLAB doesn't allow me to create such a vector to solve the equation.
Any ideas?

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回答（1 个）

Torsten
Torsten 2018-10-30
B is the unknown vector, A and X are given ?
Note that B can be determined by backward substitution:
n = 65000;
B = zeros(n,1);
B(n) = 0.5*X(n);
for i = n-1:-1:1
B(i) = (X(i)-B(i+1))*0.5
end
No need to form A explicitly.
Best wishes
Torsten.
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Torsten
Torsten 2018-10-30
If I'm not mistaken, you were first talking about a diagonal of 2's and 1's above the diagonal. Now I read that there are 1's also below the diagonal. For this case, the code from above does not work.
Try
http://www.math.iit.edu/~fass/matlab/html/TridisolveDemo.html
Best wishes
Torsten.

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