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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 347 (11 self)
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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
Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order
 in Stochastic Analysis and Related Topics VI: The Geilo Workshop
, 1996
"... The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs have ..."
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Cited by 260 (15 self)
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The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs
A Unified Framework for Hybrid Control: Model and Optimal Control Theory
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decisionmaking at the highest. Virtually all control systems todayfrom flight control to the factory floorperform computercoded chec ..."
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Cited by 305 (9 self)
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differential equations and automata, governed by a hybrid controller that issues continuousvariable commands and makes logical decisions. We first identify the phenomena that arise in realworld hybrid systems. Then, we introduce a mathematical model of hybrid systems as interacting collections of dynamical
Loewy decomposition of linear thirdorder PDE’s in the plane
 Proc. Intern. Symp. Symbolic, Algebr. Comput., ACM
, 2008
"... Loewy’s decomposition of a linear ordinary differential operator as the product of largest completely reducible components is generalized to partial differential operators of order three in two variables. This is made possible by considering the problem in the ring of partial differential operato ..."
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Cited by 2 (2 self)
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Loewy’s decomposition of a linear ordinary differential operator as the product of largest completely reducible components is generalized to partial differential operators of order three in two variables. This is made possible by considering the problem in the ring of partial differential
Practical LossResilient Codes
, 1997
"... We present a randomized construction of lineartime encodable and decodable codes that can transmit over lossy channels at rates extremely close to capacity. The encoding and decoding algorithms for these codes have fast and simple software implementations. Partial implementations of our algorithms ..."
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Cited by 284 (25 self)
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set of differential equations. The solution to these equations can then be expressed as p...
Solving ForwardBackward Stochastic Differential Equations Explicitly – a Four Step Scheme
 Prob. Th. Rel. Fields
, 1994
"... Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability ..."
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Cited by 243 (19 self)
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Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability
Cryptanalysis of block ciphers with overdefined systems of equations
, 2002
"... Abstract. Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small Sboxes interconnected by linear keydependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on proba ..."
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Cited by 253 (22 self)
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Abstract. Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small Sboxes interconnected by linear keydependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based
PETSc users manual
 ANL95/11  Revision 2.1.0, Argonne National Laboratory
, 2001
"... tract W31109Eng38. 2 This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on highperformance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provid ..."
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Cited by 282 (20 self)
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tract W31109Eng38. 2 This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on highperformance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines
Operations for Learning with Graphical Models
 Journal of Artificial Intelligence Research
, 1994
"... This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Wellknown examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models ..."
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Cited by 276 (13 self)
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are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
, 2008
"... ... reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primaldual) Galerkin projection onto a lowdimensional space associated with a smooth “parametric ..."
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Cited by 204 (37 self)
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... reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primaldual) Galerkin projection onto a lowdimensional space associated with a smooth
Results 11  20
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11,710