On the optimality of double-bracket flows
نویسندگان
چکیده
In this paper we analyse optimality of the stable fixed point of the double bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schatten p-norms.
منابع مشابه
Optimality of double bracket and generalized double bracket flows
In this paper we consider the optimal structure of double bracket flows and generalisations of these flows to more complex gradient flows. We discuss different notions of optimality and the relationship of the flows to the structure of convex polytopes.
متن کاملAccessibility of a Class of Generalized Double-bracket Flows
We investigate a generalization of Brockett’s celebrated double bracket flow that is closely related to matrix Riccati differential equations. Using known results on the classification of transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility of the generalized double bracket flow on Grassmann manifolds are derived. This leads to sufficient Lie...
متن کاملGradient Flows and Double Bracket Equations
A unified extension of the gradient flows and the double bracket equations of ChuDriessel and Brockett is obtained in the frame work of reductive Lie groups. We examine the gradient flows on the orbit in the Cartan subspace of a reductive Lie algebra, under the adjoint action. The results of Chu-Driessel and Brockett are corresponding to the reductive groups GL(n,R) and O(p, q).
متن کاملAspects of generalized double-bracket flows
In this paper we analyse generalizations of double-bracket flows to more complex isospectral equations of the form Y ′ = [Y , [G(Y −N ), Y ]], t ≥ 0, over real symmetric matrices. The new flows possess a nontrivial equilibrium structure which we explore. We discuss the stability of these equilibria. We also discuss the relationship of the new flows to the structure of (convex) Horn–Schur polyto...
متن کاملCompletely Integrable Gradient Flows
In this paper we exhibit the Toda lattice equations in a double bracket form which shows they are gradient flow equations (on their isospectral set) on an adjoint orbit of a compact Lie group. Representations for the flows are given and a convexity result associated with a momentum map is proved. Some general properties of the double bracket equations are demonstrated, including a discussion of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004