Accessibility of a Class of Generalized Double-Bracket Flows
نویسندگان
چکیده
منابع مشابه
Accessibility 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 کاملOptimality 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 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 کاملOn the Discretization of Double-Bracket Flows
This paper extends the method of Magnus series to Lie-algebraic equations originating in double-bracket ows. We show that the solution of the isospec-tral ow Y 0 = Y; N]; Y ], Y (0) = Y0 2 Sym(n), can be represented in the form Y (t) = e (t) Y0e ?(t) , where the Taylor expansion of can be constructed explicitly , term-by-term, identifying individual expansion terms with certain rooted trees wit...
متن کاملOn the optimality of double-bracket flows
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Information and Systems
سال: 2008
ISSN: 1526-7555,2163-4548
DOI: 10.4310/cis.2008.v8.n2.a5