An Implicit Riemannian Trust-Region Method for the Symmetric Generalized Eigenproblem
نویسندگان
چکیده
The recently proposed Riemannian Trust-Region method can be applied to the problem of computing extreme eigenpairs of a matrix pencil, with strong global convergence and local convergence properties. This paper addresses inherent inefficiencies of an explicit trustregion mechanism. We propose a new algorithm, the Implicit Riemannian Trust-Region method for extreme eigenpair computation, which seeks to overcome these inefficiencies while still retaining the favorable convergence properties.
منابع مشابه
Implicit Riemannian trust-region method for symmetric generalized eigenproblems
We have recently proposed a manifold-based trust-region method to compute extreme eigenpairs of symmetric matrix pencils [3]. The general optimization method had been shown [1, 2] to enjoy strong global and local convergence properties, which are inherited by its ”brute force” application to the extreme eigenproblem. However, the trust-region mechanism, which restricts the norm of the update in...
متن کاملAn implicit trust-region method on Riemannian manifolds§
We propose and analyze an “implicit” trust-region method in the general setting of Riemannian manifolds. The method is implicit in that the trust-region is defined as a superlevel set of the ρ ratio of the actual over predicted decrease in the objective function. Since this method potentially requires the evaluation of the objective function at each step of the inner iteration, we do not recomm...
متن کاملA Riemannian symmetric rank-one trust-region method
The well-known symmetric rank-one trust-region method—where the Hessian approximation is generated by the symmetric rank-one update—is generalized to the problem of minimizing a real-valued function over a d-dimensional Riemannian manifold. The generalization relies on basic differential-geometric concepts, such as tangent spaces, Riemannian metrics, and the Riemannian gradient, as well as on t...
متن کاملA truncated - CG style method for symmetric generalized eigenvalue problems 1
A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil (A, B). The leftmost or the rightmost eigenvalue can be targeted. Knowledge of (A, B) is only required through a routine that performs matrix-vector products. The method has excellent global convergence properties and its local rate of convergence is superlinear. It is based on a ...
متن کاملCommutative curvature operators over four-dimensional generalized symmetric spaces
Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.
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:
دوره شماره
صفحات -
تاریخ انتشار 2006