A Bound on the Solution to a Structured Sylvester Equation with an Application to Relative Perturbation Theory
نویسنده
چکیده
Assuming only that the spectra of A and B are disjoint as opposed to the more restrictive assumption previously used, we obtain a bound in all unitarily invariant norms on the solution to the structured Sylvester equation AX − XB = A1/2EB1/2. This bound is the first of its kind in all unitarily invariant norms under only the disjointedness assumption. An application of the bound to the relative perturbation theory for scaled Hermitian eigenvalue problems is given.
منابع مشابه
On the solving of matrix equation of Sylvester type
A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the ...
متن کاملPerturbation Theory and Backward Error
Because of the special structure of the equations AX XB = C the usual relation for linear equations "backward error = relative residual" does not hold, and application of the standard perturbation result for Ax = b yields a perturbation bound involving sep (A, B)x that is not always attainable. An expression is derived for the backward error of an approximate solution Y; it shows that the backw...
متن کاملNonresonant Excitation of the Forced Duffing Equation
We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...
متن کاملTHE APPLICATION OF THE VARIATIONAL HOMOTOPY PERTURBATION METHOD ON THE GENERALIZED FISHER'S EQUATION
In this paper, we consider the variational homotopy perturbation method (VHPM) to obtain an approximate series solution for the generalized Fisher’s equation which converges to the exact solution in the region of convergence. Comparisons are made among the variational iteration method (VIM), the exact solutions and the proposed method. The results reveal that the proposed method is very effectiv...
متن کاملA modified homotopy perturbation method to periodic solution of a coupled integrable dispersionless equation
In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 21 شماره
صفحات -
تاریخ انتشار 2000