Hello,
I am using ILU factorization as the preconditioner of a Bi-CGSTAB solver for solving a linear system of equations Ax=b. The preconditioner matrix M=(LU)^-1 is calculated by backward substitution method, solving Ly=c and Us=y. However, when A has zero diagonal elements (e.g. A(2,2) = 0) U will also have zero diagonal elements ( U(2,2 )=0) ,which makes M impossible to be solved by the backward substitution method.
How could I reorder my system of equation in order to tackle this problem?
Dear Parsa Ghofrani ,
According to your assumptions, we have n distinct equations.
To reach your request proceed as the following:
Rearrange the equations as follows:
1). The coefficient of the first unknown in the first equation is not zero.
2).The coefficient of the second unknown in the second equation is not zero.
etc
n).The coefficient of the nth-unknown in the nth-equation is not zero.
The new augmented matrix guaranteed your request.
Otherwise, if your matrix is full of zeros and det(A) =0, then the system has
i). No solution
or
ii) Infinite number of solutions.
Best regards
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