Glg. Sleijpen et Ha. Vandervorst, A JACOBI-DAVIDSON ITERATION METHOD FOR LINEAR EIGENVALUE PROBLEMS, SIAM journal on matrix analysis and applications, 17(2), 1996, pp. 401-425
In this paper we propose a new method for the iterative computation of
a few of the extremal eigenvalues of a symmetric matrix and their ass
ociated eigenvectors. The method is based on an old and almost unknown
method of Jacobi. Jacobi's approach, combined with Davidson's method,
leads to a new method that has improved convergence properties and th
at may be used for general matrices. We also propose a variant of the
new method that may be useful for the computation of nonextremal eigen
values as well.