On the Least Squares Solution of Inverse Eigenvalue Problems

Authors:
Xuzhou Chen;Moody T. Chu
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1996

Citing 0
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Abstract

An inverse eigenvalue problem, where a matrix is to be constructed from some or all of its eigenvalues, may not have a real-valued solution at all. An approximate solution in the sense of least squares is sometimes desirable. Two types of least squares problems are formulated and explored in this paper. In spite of their different appearance, the two problems are shown to be equivalent. Thus one new numerical method, modified from the conventional alternating projection method, is proposed. The method converges linearly and globally and can be used to generate good starting values for other faster but more expensive and locally convergent methods. The idea can be applied to multiplicative inverse eigenvalue problems for the purpose of preconditioning. Numerical examples are presented.