This paper analyzes the influences of the deflation on the accuracy of the com pared eigenvalues of matrix. Based on the Rayleigh quotient theory, we proved that the influences, Generally speaking, are less important.
The Condition numbers are defined for the stabilizing Solutions of Continuoustime, discrete-time and the reverse discrete-time algebraic Riccati equations. The first-order perturbation expansions for the stabilizing Solutions are also obtained.
This paper deals with the sensitivity analysis of the system Hessenberg form, the square reduced factorization of a Hamiltonian matrix, and the QT decomposition of a symplectic matrix. By local expansition, the condition numbers are defined.
This paper concerns with measures of the sensitivity of a nondefective multiple generalized eigenvalue of a regular matrix-pair. Wilkinson condition numbers are introduced and some related properties are studied, especially, the Wilkinson’s theorem on matrices with a very ill-conditioned eigenproblem is extended. A Gerschgorin-Weyl typed theorem is established. These results are useful to analyse the accuracy of computed eigenvalues.
