Efficient Transformation of the General 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 (Univeristy of Wuppertal) who modified Crawford’s algorithm and implemented this procedure to ELPA. 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 (Univeristy of Wuppertal) who modified Crawford’s algorithm and implemented this procedure to...     »