Description
This presentation examines the asymptotic behavior of matrix iterations, focusing on the QR and LR algorithms and their significance in eigenvalue computation. It highlights foundational developments by Rutishauser, Francis, and Kublanovskaya and modern refinements by Huang and Tam, particularly on matrix decompositions and spectral properties. Extensions of Yamamoto’s theorem, including recent works by Nayak and Shekhawat, and Huang and Tam, are discussed, connecting iterative processes to spectral radius formulas and Jordan decompositions. This is a joint work with Huajun Huang of Auburn University.
Date of Event
Thursday, February 6, 2025
Location
Parker Building 338
Included in
Asymptotic Matrix Behaviors and Iterative Algorithms
Parker Building 338
This presentation examines the asymptotic behavior of matrix iterations, focusing on the QR and LR algorithms and their significance in eigenvalue computation. It highlights foundational developments by Rutishauser, Francis, and Kublanovskaya and modern refinements by Huang and Tam, particularly on matrix decompositions and spectral properties. Extensions of Yamamoto’s theorem, including recent works by Nayak and Shekhawat, and Huang and Tam, are discussed, connecting iterative processes to spectral radius formulas and Jordan decompositions. This is a joint work with Huajun Huang of Auburn University.
Presenter Bio
Prof. Tin-Yau Tam is a Department Chair & Professor and the Seneca C. and Mary B. Weeks Chair in Mathematics, at the University of Nevada, Reno, USA. He obtained his B.Sc. in Mathematics from the University of Hong Kong in 1982, and his Ph.D. in Mathematics also from the University of Hong Kong in 1986. Prof. Tam’s research interests are in Matrix Theory, Lie Groups and Lie Algebra, Multilinear Algebra, Numerical Range, Operator Theory and Applications. He currently serves on multiple editorial boards of Mathematics Journals. Prof. Tam’s extensive work and accomplishments can be found in his website: https://sites.google.com/view/tinyautam/homepage.