منابع مشابه
Diagonalizable Quadratic Eigenvalue Problems
A system is defined to be an n× n matrix function L(λ) = λ2M + λD +K where M, D, K ∈ Cn×n and M is nonsingular. First, a careful review is made of the possibility of direct decoupling to a diagonal (real or complex) system by applying congruence or strict equivalence transformations to L(λ). However, the main contribution is a complete description of the much wider class of systems which can be...
متن کاملAlgorithms for hyperbolic quadratic eigenvalue problems
We consider the quadratic eigenvalue problem (QEP) (λ2A+λB+ C)x = 0, where A,B, and C are Hermitian with A positive definite. The QEP is called hyperbolic if (x∗Bx)2 > 4(x∗Ax)(x∗Cx) for all nonzero x ∈ Cn. We show that a relatively efficient test for hyperbolicity can be obtained by computing the eigenvalues of the QEP. A hyperbolic QEP is overdamped if B is positive definite and C is positive ...
متن کاملDetecting and Solving Hyperbolic Quadratic Eigenvalue Problems
Hyperbolic quadratic matrix polynomials Q(λ) = λ2A + λB + C are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with nonpositive eigenvalues. Neither the definition of overdamped nor any of the standard characterizations provides an efficient way to test if a given Q has this property. We show that a quadratically converg...
متن کاملElliptic and hyperbolic quadratic eigenvalue problems and associated distance problems
Two important classes of quadratic eigenvalue problems are composed of elliptic and hyperbolic problems. In [Linear Algebra Appl., 351–352 (2002) 455], the distance to the nearest non-hyperbolic or non-elliptic quadratic eigenvalue problem is obtained using a global minimization problem. This paper proposes explicit formulas to compute these distances and the optimal perturbations. The problem ...
متن کاملContinuation of Invariant Subspaces for Parameterized Quadratic Eigenvalue Problems
We consider quadratic eigenvalue problems with large and sparse matrices depending on a parameter. Problems of this type occur, for example, in the stability analysis of spatially discretized and parameterized nonlinear wave equations. The aim of the paper is to present and analyze a continuation method for invariant subspaces that belong to a group of eigenvalues the number of which is much sm...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1988
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700026824