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Sum Capacity of a Gaussian Vector Broadcast Channel
 IEEE Trans. Inform. Theory
, 2002
"... This paper characterizes the sum capacity of a class of nondegraded Gaussian vectB broadcast channels where a singletransmitter with multiple transmit terminals sends independent information to multiple receivers. Coordinat+[ is allowed among the transmit teminals, but not among the different recei ..."
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Cited by 279 (21 self)
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class of Gaussian channels whose saddlepoint satisfies a full rank condition. Furt her,t he sum capacity is achieved using a precoding method for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown t correspond to a decision
Saddlepoint Solution of the Fingerprinting Capacity Game Under the Marking Assumption
"... Abstract — We study a fingerprinting game in which the collusion channel is unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value o ..."
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Cited by 16 (2 self)
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sum game, and show that it is achieved by a saddlepoint. If the coalition size is k and the fingerprint alphabet is binary, we derive equations that can solve the capacity game for arbitrary k. We also show that the capacity Ck,2 satisfies (k 2 2 ln 2) −1 ≤ Ck,2 ≤ (k 2 ln 2) −1. By examining the saddlepoint
Generating functions and the satisfiability threshold
"... The 3SAT problem consists in determining if a boolean formula with 3 literals per clause is satisfiable. When the ratio between the number of clauses and the number of variables increases, a threshold phenomenon is observed: the probability of satisfiability appears in simulations to decrease sharp ..."
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Cited by 2 (0 self)
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in the 3SAT problem. Recent works have provided so far upper and lower bounds for the threshold’s potential location. We present here a unified approach to upper bounds that is based on urn models, generating functions, and saddlepoint bounds. No new upper bound is presented here but instead, we show
Adaptive Wavelet Methods For Saddle Point Problems  Optimal Convergence Rates
 IGPM report, RWTH Aachen
, 2001
"... In this paper an adaptive wavelet scheme for saddle point problems is developed and analysed. Under the assumption that the underlying continuous problem satisfies the infsup condition it is shown in the first part under which circumstances the scheme exhibits asymptotically optimal complexity. Thi ..."
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Cited by 45 (18 self)
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In this paper an adaptive wavelet scheme for saddle point problems is developed and analysed. Under the assumption that the underlying continuous problem satisfies the infsup condition it is shown in the first part under which circumstances the scheme exhibits asymptotically optimal complexity
Complements on Hilbert Spaces and Saddle Point Systems
 Journal of Computational and Applied Mathematics, Volume 225, Issue
"... For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility LadyshenskayaBabušcaBrezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators onl ..."
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Cited by 8 (8 self)
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symmetric saddle point problem, the inexact Uzawa algorithm converges provided that the inexact process for inverting the residual at each step has the relative error smaller than 1/3. As a consequence, we provide a new type of algorithm for discretizing saddle point problems, which combines the inexact
AN IMPLICIT APPROXIMATE INVERSE PRECONDITIONER FOR SADDLE POINT PROBLEMS ∗
"... Abstract. We present a preconditioner for saddle point problems which is based on an approximation of an implicit representation of the inverse of the saddle point matrix. Whereas this preconditioner does not require an approximation to the Schur complement, its theoretical analysis yields some inte ..."
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of the preconditioned system satisfy the constraint equations exactly. We will demonstrate the performance of the implicit approximate inverse preconditioner in the iterative solution of the discrete two as well as threedimensional Oseen equations. Key words. saddle point problem, preconditioning AMS subject
Multilevel discretization of Symmetric Saddle Point Systems without the discrete LBB Condition
"... Using an inexact Uzawa algorithm at the continuous level, we study the convergence of multilevel algorithms for solving saddlepoint problems. The discrete stability LadyshenskayaBabušcaBrezzi (LBB) condition does not have to be satisfied. The algorithms are based on the existence of a multilevel ..."
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Cited by 3 (3 self)
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Using an inexact Uzawa algorithm at the continuous level, we study the convergence of multilevel algorithms for solving saddlepoint problems. The discrete stability LadyshenskayaBabušcaBrezzi (LBB) condition does not have to be satisfied. The algorithms are based on the existence of a
Homology of saddle point reduction and applications to resonant elliptic systems ∗
"... In the setting of saddle point reduction, we prove that the critical groups of the original functional and the reduced functional are isomorphic. As application, we obtain two nontrivial solutions for elliptic gradient systems which may be resonant both at the origin and at infinity. The difficulty ..."
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that the variational functional does not satisfy the PalaisSmale condition is overcame by taking advantage of saddle point reduction. Our abstract results on critical groups are crucial.
A PredictorCorrector Algorithm For A Class Of Nonlinear Saddle Point Problems
 SIAM Journal on Control and Optimization
, 1994
"... . An interior pathfollowing algorithm is proposed for solving the nonlinear saddle point problem minimax c T x + OE(x) + b T y \Gamma /(y) \Gamma y T Ax subject to (x; y) 2 X \Theta Y ae R n \Theta R m ; where OE(x) and /(y) are smooth convex functions and X and Y are boxes (hyperrecta ..."
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Cited by 5 (2 self)
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of the problem in O( p m+ nj log ¯=fflj) iterations if both OE(x) and /(y) satisfy a scaled Lipschitz condition. Keywords. Interior point methods, optimal control, saddle point problem, stochastic programming. Abbreviated title. IP method for saddle point problems AMS subject classifications. 49J35, 65K10, 90
Preconditioning of saddle point systems by substructuring and a penalty approach
 Domain Decomposition Methods in Sciences and Engineering XVI, number 55 in Lecture Notes in Computational Science and Engineering
, 2006
"... Summary. The focus of this paper is a penaltybased strategy for preconditioning elliptic saddle point systems. As the starting point, we consider the regularization approach of Axelsson in which a related linear system, differing only in the (2,2) block of the coefficient matrix, is introduced. By ..."
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Cited by 6 (2 self)
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Summary. The focus of this paper is a penaltybased strategy for preconditioning elliptic saddle point systems. As the starting point, we consider the regularization approach of Axelsson in which a related linear system, differing only in the (2,2) block of the coefficient matrix, is introduced
Results 1  10
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111