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A Numerical Study of Globalizations of NewtonGMRES Methods
, 2003
"... Newton’s method is at the core of many algorithms used for solving nonlinear equations. A globalized Newton method is an implementation of Newton’s method augmented with “globalization procedures ” intended to enhance the likelihood of convergence to a solution from an arbitrary initial guess. A Ne ..."
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Cited by 1 (0 self)
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robust and efficient algorithms for solving nonlinear equations. The aim of this project is to describe the development of some globalized NewtonGMRES methods and to compare their performances on a few benchmark fluid flow problems. i Acknowledgments I was first introduced to the topic of Numerical
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 582 (23 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first
Some convergence results for the NewtonGMRES algorithm
, 1993
"... : In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction in ..."
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Cited by 2 (2 self)
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: In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction
Some convergence results for the NewtonGMRES algorithm
, 1993
"... : In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction in ..."
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: In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
On backtracking failure in NewtonGMRES methods with a demonstration for the NavierStokes equations
 J. of Comp. Phy
"... In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier– Stokes equations with heat and mass transport. Specifically, it was observed that a Newton–GMRES method globalized by backtracking (linese ..."
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Cited by 9 (0 self)
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In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier– Stokes equations with heat and mass transport. Specifically, it was observed that a Newton–GMRES method globalized by backtracking
An introduction to variational methods for graphical models
 TO APPEAR: M. I. JORDAN, (ED.), LEARNING IN GRAPHICAL MODELS
"... ..."
Vivaldi: A Decentralized Network Coordinate System
 In SIGCOMM
, 2004
"... Largescale Internet applications can benefit from an ability to predict roundtrip times to other hosts without having to contact them first. Explicit measurements are often unattractive because the cost of measurement can outweigh the benefits of exploiting proximity information. Vivaldi is a simp ..."
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Cited by 593 (5 self)
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Largescale Internet applications can benefit from an ability to predict roundtrip times to other hosts without having to contact them first. Explicit measurements are often unattractive because the cost of measurement can outweigh the benefits of exploiting proximity information. Vivaldi is a
Mean shift, mode seeking, and clustering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeki ..."
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Cited by 620 (0 self)
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seeking process on a surface constructed with a “shadow ” kernel. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis is treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications
Results 1  10
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