An extension of the Cayley transform method for a parameterized generalized inverse eigenvalue problem. Issue 6 (10th August 2020)

• Record Type: Journal Article
• Authors: Dalvand, Zeynab; Hajarian, Masoud; Roman, Jose E.
• Is Part Of: Numerical linear algebra with applications. Volume 27:Issue 6(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-08-10
• Subjects: Cayley transform -- parameterized generalized inverse eigenvalue problem -- QR‐like decomposition; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2327
• Languages: English
• ISSNs: 1070-5325

Abstract

Summary: Since recent studies have shown that the Cayley transform method can be an effective iterative method for solving the inverse eigenvalue problem, in this work, we consider using an extension of it for solving a type of parameterized generalized inverse eigenvalue problem and prove its locally quadratic convergence. This type of inverse eigenvalue problem, which includes multiplicative and additive inverse eigenvalue problems, appears in many applications. Also, we consider the case where the given eigenvalues are multiple. In this case, we describe a modified problem that is not overdetermined and discuss the extension of the Cayley transform method for this modified problem. Finally, to demonstrate the effectiveness of these algorithms, we present some numerical examples to show that the proposed methods are practical and efficient.