Multi-sweep Algorithms for the Symmetric Eigenproblem

Wilfried N. Gansterer, Dieter F. Kvasnicka, Christoph W. Ueberhuber

Abstract: This paper shows how the symmetric eigenproblem, which is the computationally most demanding part of numerous scientific and industrial applications, can be solved much more efficiently than by using algorithms currently implemented in Lapack routines. The main techniques used in the algorithm presented in this paper are (i) sophisticated blocking in the tridiagonalization, which leads to a two-sweep algorithm; and (ii) the computation of the eigenvectors of a band matrix instead of a tridiagonal matrix. This new algorithm improves the locality of data references and leads to a significant improvement of the floating-point performance of symmetric eigensolvers on modern computer systems. Speedup factors of up to four (depending on the computer architecture and the matrix size) have been observed.