A new algorithm for computing the inertia of eigenproblems (Ax=λx) and (Ax=λBx)

摘要

The inertia of a n×n complex matrix A, is defined to be an integer triple, In(A)=(π(A),ν(A),δ(A)), where π(A) is the number of eigenvalues of A with positive real parts, ν(A) is the number of eigenvalues with negative real parts and δ(A) is the number of eigenvalues with zero real parts.In this paper we show that the inertia can be computed by Gereshgorin theorem and block shift-and-invert algorithm for equation Ax=λBx or Ax=λx and this algorithm is compared by function eig.m and sptarn.m in Matlab.