Nonlinear Low Rank Modification of a Symmetric Eigenvalue Problem
نویسندگان
چکیده
This paper studies existence and uniqueness results and interlacing properties of nonlinear modifications of small rank of symmetric eigenvalue problems. Approximation properties of the Rayleigh functional are used to design numerical methods the local convergence of which is quadratic or even cubic. Numerical examples demonstrate their efficiency.
منابع مشابه
Nonlinear Rank-one Modification of the Symmetric Eigenvalue Problem
Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteratio...
متن کاملSome results on the symmetric doubly stochastic inverse eigenvalue problem
The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
متن کاملAn Accelerated Greedy Missing Point Estimation Procedure
Model reduction via Galerkin projection fails to provide considerable computational savings if applied to general nonlinear systems. This is because the reduced representation of the state vector appears as an argument to the nonlinear function, whose evaluation remains as costly as for the full model. Masked projection approaches, such as the missing point estimation and the (discrete) empiric...
متن کاملEla the Minimum Rank Problem over Finite Fields
The problem of finding mr(F,G) and describing Gk(F ) has recently attracted considerable attention, particularly for the case in which F = R (see [29, 17, 26, 25, 27, 13, 33, 5, 9, 22, 2, 11, 6, 7, 10, 18, 4]). The minimum rank problem over R is a sub-problem of a much more general problem, the inverse eigenvalue problem for symmetric matrices: given a family of real numbers, find every symmetr...
متن کاملSolving Rational Eigenvalue Problems via Linearization
The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 32 شماره
صفحات -
تاریخ انتشار 2011