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I am looking for a LAPACK routine that allows to find a non-trivial solution to the following equation:
A x = 0
provided that A is a n×n square singular non-symmetric band matrix.
In reality A matrix may not be exactly singular as it is based on some parameter and I use a root finding algorithm to find this parameter (requiring det(A) = 0, where the determinant is found with DGBTRF and multiplication of the diagonal elements).
The only solution I have came up so far is to consider A a dense matrix matrix, use DGEEV to find its eigenvalues and eigenvectors and take the eigenvector for the eigenvalue closest to zero. However, I believe this is strongly sub-optimal approach. Can anyone suggest a better one?