A new method for assigning, the eigenvalues sign in equations (Ax = λx) and (Ax = λBx)

  • Authors:

  • Hashem Saberi Najafi;Maryam Shams Solary

  • Affiliations:

  • Guilan University, Computer Center, Rasht, Iran;Guilan University, Department of Mathematics, Faculty of Sciences, Rasht, Iran

  • Venue:
  • ACS'08 Proceedings of the 8th conference on Applied computer scince
  • Year:
  • 2008

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Abstract

The inertia of an n × n complex matrix A, is defined to be an integer triple In(A) = (π(A), v(A), δ(A)) where π(A) is the number of eigenvalues of A with positive real parts, v(A) is the number of eigenvalues with negative real parts and δ(A) is the number of eigenvalues with zero real parts. We are interested in computing the Inertia for large unsymmetric generalized eigenproblem (A,B) for equation Aϕ = λBϕ Where A and B are n × n large matrices. For standard eigenvalues problem let B = Identity matrix. An obvious approach for determine Inertia of pair(A,B), is to transform this to a standard eigenproblem by inverting either A or B. In this paper we show that the eigenvalues sign can be computed by assigning the interval that including all the eigenvalues and this method is compared by results in Matlab.