Paper Title:

Recursive Bounds for the Eigenvalues of Symmetric Positive Definite Matrices

Author(s):

Pravin Singh, Shivani Singh, Virath Singh

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

University of South Africa,
Department of Decision Sciences, PO Box 392,
 Pretoria,0003,
South Africa.

University of KwaZulu-Natal,
Private Bag X54001,
Durban, 4001,
South Africa.

E-mail: singhp@ukzn.ac.za, singhs2@unisa.ac.za, singhv@ukzn.ac.za
 

Abstract:

In this paper, we bound the extremal eigenvalues of a positive definite real symmetric matrix by considering a part of the characteristic equation in the region of the smallest and largest eigenvalues. An expansion around these values leads to a sequence of monotonic functions, whose zeros coincide with the extremal zeros of associated polynomials. The latter is shown to yield bounds that are fairly accurate.

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