TOPICS ON A GENERALIZATION OF GERSHGORIN THEOREM

We construct two classes of 3 X 3 and 4 X 4 real symmetric matrices, a nd establish sufficient conditions for the spectrum of a matrix A in e ach class to be disjoint from its kth order Gershgorin region. This pr ovides a partial answer to a question raised by Newman and Thompson. T he problem of providing sufficient conditions for the localization of the spectrum of a matrix in its kth order Gershgorin region is also di scussed. (C) 1998 Elsevier Science Inc.