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A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 345 (11 self)
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to be developed in order to allow an efficient solution of even larger problems. This paper gives a review of the first hierarchical and purely matrixbased approach, algebraic multigrid (AMG). AMG can directly be applied, for instance, to efficiently solve various types of elliptic partial differential equations
Parallel LagrangeNewtonKrylovSchur methods for PDEconstrained optimization. Part I: The KrylovSchur solver
 SIAM J. Sci. Comput
, 2000
"... Abstract. Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for such problems is reduced quasiNewton sequential quadratic programming (SQP) methods. These methods take full advantage of existin ..."
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Cited by 113 (19 self)
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a symmetric quasiminimum residual method; preconditioning of the KKT system using an approximate state/decision variable decomposition that replaces the forward PDE Jacobians by their own preconditioners, and the decision space Schur complement (the reduced Hessian) by a BFGS approximation or by a
Schwarz Analysis Of Iterative Substructuring Algorithms For Elliptic Problems In Three Dimensions
 SIAM J. Numer. Anal
, 1993
"... . Domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations of partial differential equations. The preconditioners are constructed from exact or approximate sol ..."
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Cited by 144 (32 self)
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. Domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations of partial differential equations. The preconditioners are constructed from exact or approximate
SecondOrder Cone Programming
 MATHEMATICAL PROGRAMMING
, 2001
"... In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic struc ..."
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Cited by 231 (11 self)
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In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic
Contributions of Issai Schur to analysis, in
 Studies in Memory of Issai Schur, xci–clxxxviii, Progr. Math
, 2003
"... The name Schur is associated with many terms and concepts that are widely used in a number of diverse fields of mathematics and engineering. This survey article focuses on Schur’s work in analysis. Here too, Schur’s name is commonplace: The Schur test and SchurHadamard multipliers (in the study of ..."
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Cited by 9 (0 self)
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The name Schur is associated with many terms and concepts that are widely used in a number of diverse fields of mathematics and engineering. This survey article focuses on Schur’s work in analysis. Here too, Schur’s name is commonplace: The Schur test and SchurHadamard multipliers (in the study
Weak FourierSchur sampling,
, 2006
"... the hidden subgroup problem, and the quantum collision problem ..."
Secure Transmission with Multiple Antennas: The MISOME Wiretap Channel
, 2007
"... The role of multiple antennas for secure communication is investigated within the framework of Wyner’s wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and t ..."
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Cited by 235 (20 self)
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The role of multiple antennas for secure communication is investigated within the framework of Wyner’s wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacityachieving. In addition, we show that in the high signaltonoise (SNR) ratio regime the penalty for not knowing eavesdropper’s channel is small—a simple “secure spacetime code ” that can be thought of as masked beamforming and radiates power isotropically attains nearoptimal performance. In the limit of large number of antennas, we obtain a realizationindependent characterization of the secrecy capacity as a function of the number β: the number of eavesdropper antennas per sender antenna. We show that the eavesdropper is comparatively ineffective when β < 1, but that for β≥2 the eavesdropper can drive the secrecy capacity to zero, thereby blocking secure communication to the intended receiver. Extensions to ergodic fading channels are also provided.
Von Neumann Algebras
, 2009
"... The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. In this sense it is opposite in spirit from the treatises of ..."
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Cited by 111 (5 self)
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The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. In this sense it is opposite in spirit from the treatises of
Results 1  10
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