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13,196
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 537 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
Strongly Elliptic Systems and Boundary Integral Equations
, 2000
"... Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematic ..."
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Cited by 501 (0 self)
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Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
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Cited by 630 (24 self)
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We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential
Elastically deformable models
 Computer Graphics
, 1987
"... The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision an ..."
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Cited by 883 (20 self)
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to control the creation and evolution of models. Mathematically, the approach prescribes systems of dynamic (ordinary and partial) differential equations to govern model behavior. These equations of motion may be
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems
, 1992
"... We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many of the examp ..."
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Cited by 460 (20 self)
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We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many
A Note on the Risch Differential Equation
"... This paper relates to the technique of integrating a function in a purely transcendental regular elementary Liouville extension by prescribing degree bounds for the transcendentals and then solving linear systems over the constants. The problem of finding such bounds explicitly remains yet to be sol ..."
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. This result provides an algorithm for solving the differential equation y 0 +f 0 y = g in y where f , g and y are rational functions over an arbitrary constant field. This new algorithm can be regarded as a direct generalization of the algorithm by E. Horowitz for computing the rational part
A Fluidbased Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED
 Proc. SIGCOMM 2000
, 2000
"... In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved numeri ..."
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Cited by 417 (21 self)
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In this paper we use jump process driven Stochastic Differential Equations to model the interactions of a set of TCP flows and Active Queue Management routers in a network setting. We show how the SDEs can be transformed into a set of Ordinary Differential Equations which can be easily solved
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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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
Results 1  10
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13,196