A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix

College

Gokongwei College of Engineering

Department/Unit

Electronics And Communications Engg

Document Type

Article

Source Title

Third Humanoid, Nanotechnology, Information Technology, Communication and Control Environment and Management (HNICEM) International Conference

Publication Date

3-2007

Physical Description

5 leaves.

Abstract

The known formula [ ] ( ) 1 1 / Tr N N λ = A , where A is an n n × Hermitian matrix, 1 λ is its dominant eigenvalue and N is a sufficiently large positive integer, is given the modification ( ) 1 1 / Tr N N λ = A . This modification is conjectured to apply to any n n × matrices, whether Hermitian or not and is converted into an algorithm for obtaining the modulus of the dominant eigenvalue of A . A heuristic basis for the correctness of the latter formula is given. Several numerical examples with graphical representations of their convergences are given, including an unusual case where ongoing steps give alternately the exact value and the successive approximations of the dominant eigenvalue.

html

Disciplines

Theory and Algorithms

Note

[Paper presented during the Third Humanoid, Nanotechnology, Information Technology, Communication and Control Environment and Management (HNICEM) International Conference, held at the Century Park Hotel, Manila, Philippines on 15-18 March 2007].

Keywords

Hermitian operators; Eigenvalues

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Upload File

wf_no

This document is currently not available here.

Share

COinS