Efficient Transformation of the generalized Eigenproblem with symmetric banded matrices to a banded standard Eigenproblem

The solution of symmetric eigenproblems plays a key role in many computational simulations. Generalized eigenproblems are transformed to a standard problem. This transformation has the drawback that for banded matrices in the generalized eigenproblem the banded structure is not preserved. The matrix of the standard eigenproblem will generally be a full matrix. We followed the ideas of the Group of Lang (University of Wuppertal) who modified Crawford’s algorithm and implemented a procedure for small bandwidth to the ELPA project. By keeping the banded structure we save one reduction step on the matrix and one backtransformation step for the eigenvectors. This provides a good speedup compared to the standard tranformation procedure with Cholesky factorization.     «

The solution of symmetric eigenproblems plays a key role in many computational simulations. Generalized eigenproblems are transformed to a standard problem. This transformation has the drawback that for banded matrices in the generalized eigenproblem the banded structure is not preserved. The matrix of the standard eigenproblem will generally be a full matrix. We followed the ideas of the Group of Lang (University of Wuppertal) who modified Crawford’s algorithm and implemented a procedure for sm...     »