Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations

New methods for computing eigenvectors of symmetric block tridiagonal matrices based on twisted block factorizations are explored. The relation of the block where two twisted factorizations meet to an eigenvector of the block tridiagonal matrix is reviewed. Based on this, several new algorithmic strategies for computing the eigenvector efficiently are motivated and designed. The underlying idea is to determine a good starting vector for an inverse iteration process from the twisted block factorizations such that a good eigenvector approximation can be computed with a single step of inverse iteration.