I have a symmetric indefinite matrix $A$ which is banded, and I want to compute the $LDL^T$ factorization, however there do not appear to exist codes to do this in standard libraries (such as LAPACK, matlab, etc). I'd prefer to use an efficient algorithm rather than use a standard $LDL^T$ code on a full/dense matrix.

I am wondering if perhaps the reason codes don't exist is because the $LDL^T$ factorization of a symmetric banded matrix does not have the same banded structure? For a symmetric positive definite banded matrix, it is true that the Cholesky factor shares the same band structure as the original matrix, and indeed there exists a LAPACK routine to compute this factorization (DPBTRF). It seems the same should be true for $LDL^T$ but am I missing something?

Also, I found this a reference here which describes the Bunch-Kaufman algorithm which computes $LDL^T$ for a symmetric indefinite band matrix. The abstract says that the algorithm does not preserve band structure. But what about the usual diagonal pivoting algorithm? Wouldn't that preserve band structure?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.