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 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 کاملBalancing Regular Matrix Pencils
In this paper we present a new diagonal balancing technique for regular matrix pencils λB − A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired from the balancing technique of a square matrix A and has a comparable complexity. Upon convergence, the diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also s...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1991
ISSN: 0377-0427
DOI: 10.1016/0377-0427(91)90183-k