Paper Title:

A New Method for Eigenvalue Computations for Positive Definite Matrices

Author(s):

Pravin Singh, Shivani Singh, Virath Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4000,
South Africa.
E-mail: singhp@ukzn.ac.za

University of South Africa, Department of Decision Sciences,
PO Box 392, Pretoria, 0003,
South Africa.
E-mail: singhs2@unisa.ac.za

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4000,
 South Africa.
E-mail: singhv@ukzn.ac.za  

Abstract:

In this paper, we derive and analyse a new method to compute the first few dominant eigenvalues of real positive definite matrices. It involves a variant of the power method, shifted inverse iteration and the innerproduct functional. Our method is shown to reconstruct the minimal polynomial of the matrix.

Full Text PDF: