A new algorithm for computing the inertia of eigenproblems (Ax = lambda x) and (Ax = lambda Bx)

作者：Najafi H Saberi^*; Solary M Shams

来源：Applied Mathematics and Computation, 2008, 201(1-2): 138-148.

DOI：10.1016/j.amc.2007.12.005

• inertia
• Arnoldi algorithm
• generalized eigenproblem
• shift-and-invert
• Gereshgorin
• block matrix

The inertia of a n x n complex matrix A, is defined to be an integer triple, In(A) = (pi(A), v(A), delta(A)), where pi(A) is the number of eigenvalues of A with positive real parts, v(A) is the number of eigenvalues with negative real parts and delta(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 = lambda Bx or Ax = lambda x and this algorithm is compared by function eig.m and sptarn.m in Matlab.

• 出版日期2008-7-15