THE STRONG STABILITY OF ALGORITHMS FOR SOLVING THE SYMMETRIC EIGENPROBLEM
Alicja Smoktunowicz · Journal of the Korea Society for Industrial and Applied Mathematics · 2003
The concepts of stability of algorithms for solving the symmetric and generalized symmetric-definite eigenproblems are discussed. An algorithm for solving the symmetric eigenproblem Ax = ‚x is stable if the computed solution z is the exact solution of some slightly perturbed system (A + E)z = ‚z. We use both normwise approach and componentwise way of measuring the size of the perturbations in data. If E preserves symmetry we say that an algorithm is strongly stable (in a normwise or componentwise sense, respectively). The relations between the stability and strong stability are investigated for some classes of matrices.