Zheng-Jian Bai et al 2004 Inverse Problems 20 1675 doi:10.1088/0266-5611/20/5/022
Zheng-Jian Bai1, Raymond H Chan1 and Benedetta Morini2
Show affiliationsThe Cayley transform method is a Newton-like method for solving inverse eigenvalue problems. If the problem is large, one can solve the Jacobian equation by iterative methods. However, iterative methods usually oversolve the problem in the sense that they require far more (inner) iterations than is required for the convergence of the Newton (outer) iterations. In this paper, we develop an inexact version of the Cayley transform method. Our method can reduce the oversolving problem and it improves the efficiency with respect to the exact version. We show that the convergence rate of our method is superlinear and that a good tradeoff between the required inner and outer iterations can be obtained.
Issue 5 (October 2004)
Received 20 February 2004, in final form 8 July 2004
Published 16 August 2004
Zheng-Jian Bai et al 2004 Inverse Problems 20 1675
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