Variational and numerical methods for symmetric matrix pencils
نویسندگان
چکیده
منابع مشابه
Rayleigh-Ritz and Lanctos Methods for Symmetric Matrix Pencils*
We are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils. First, Rayleigh-Ritz methods are formulated and, using Krylov subspaces, a convergence analysis is presented for definite pencils. Second, generalized symmetric Lanczos algorithms are introduced as a special Rayleigh-Ritz method. In particular, an a posteriori convergence criterion is demonstrated by...
متن کاملSymplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...
متن کاملOrbit Closure Hierarchies of Skew-symmetric Matrix Pencils
We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skewsymmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another ske...
متن کاملEla Symmetric Matrix Pencils: Codimension Counts and the Solution of a Pair of Matrix Equations∗
The set of all solutions to the homogeneous system of matrix equations (XA + AX,XB +BX) = (0,0), where (A,B) is a pair of symmetric matrices of the same size, is characterized. In addition, the codimension of the orbit of (A,B) under congruence is calculated. This paper is a natural continuation of the article [A. Dmytryshyn, B. K̊agström, and V.V. Sergeichuk. Skew-symmetric matrix pencils: Codi...
متن کاملSymmetric matrix pencils: codimension counts and the solution of a pair of matrix equations
The set of all solutions to the homogeneous system of matrix equations (XA + AX,XB +BX) = (0,0), where (A,B) is a pair of symmetric matrices of the same size, is characterized. In addition, the codimension of the orbit of (A,B) under congruence is calculated. This paper is a natural continuation of the article [A. Dmytryshyn, B. K̊agström, and V.V. Sergeichuk. Skew-symmetric matrix pencils: Codi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1991
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700028732