Least-squares solutions of constrained inverse eigenproblem and associated optimal approximation problem

Abstract

In this paper, the least-squares solutions of constrained inverse eigenvalue problem and the associated optimal approximation problem are considered. We get the general expression of the least-squares solutions of the constrained inverse eigenvalue problem, obtain the representation of the unique optimal approximation solution in the least-squares solutions set, and give the algorithm and corresponding computational examples.

Keywords:

• least-squares solution
• inverse eigenvalue problem
• optimal approximation
• singular value decomposition
• constrained solution

2010 AMS Subject Classifications:

• 65F15
• 65F18
• 15A18
• 15A29

Acknowledgements

A Project Supported by Hunan Provincial Natural Science Foundation of China. NO.09JJ6012.