In [9] it was shown that it is possible to construct eigenvalue algorthms based on Newton's method and inverse iteration which can result in second-and even thirdorder rates of convergence, with applications to nonlinear problems also possible. Recently, the use of these methods for large-scale problems was considered [2]. The difficulty is that these methods require matrix factorization at each iteration and become prohitively epensive of good initial estimates are not availabel.
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