A Saddle Point Theorem for Self-dual Linear Systems
نویسندگان
چکیده
Let A be a skew matrix of order n over an ordered field. There Is a finite class of skew matrices A such that XA = Y and XA = Y have the same solution sets, where x = y. and y = x for some Indices 1 (perhaps none) and x = x , y = y for the remaining 1 . We show that for each Index h, 1 < h < n, there exists an A such that ä > 0 for all J . A proof of von Neumann's Mlnlmax Theorem for symmetric games Is one application of the theory.
منابع مشابه
Hamiltonian Trajectories and Duality in the Optimal Control of Linear Systems with Convex Costs
A duality theorem is proved for problems of optimal control of linear dynamical systems in continuous time subject to linear constraints and convex costs, such as penalties. Optimality conditions are stated in terms of a “minimaximum principle” in which the primal and dual control vectors satisfy a saddle point condition at almost every instant of time. This principle is shown to be equivalent ...
متن کاملConjugate gradient method for dual-dual mixed formulations
We deal with the iterative solution of linear systems arising from so-called dual-dual mixed finite element formulations. The linear systems are of a two-fold saddle point structure; they are indefinite and ill-conditioned. We define a special inner product that makes matrices of the two-fold saddle point structure, after a specific transformation, symmetric and positive definite. Therefore, th...
متن کاملShortcut Node Classification for Membrane Residue Curve Maps
comNode classification within Membrane Residue Curves (M-RCMs) currently hinges on Lyapunov’s Theorem and therefore the computation of mathematically complex eigenvalues. This paper presents an alternative criterion for the classification of nodes within M-RCMs based on the total membrane flux at node compositions. This paper demonstrates that for a system exhibiting simple permeation behaviour...
متن کاملABS Solution of equations of second kind and application to the primal-dual interior point method for linear programming
Abstract We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS cl...
متن کاملConvergence Properties of Hermitian and Skew Hermitian Splitting Methods
In this paper we consider the solutions of linear systems of saddle point problems. By using the spectrum of a quadratic matrix polynomial, we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method.
متن کامل