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Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
Abstract

Cited by 555 (12 self)
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This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than restricting attention to traditional nonlinear least squares.
Unified analysis of discontinuous Galerkin methods for elliptic problems
 SIAM J. Numer. Anal
, 2001
"... Abstract. We provide a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment ..."
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Cited by 519 (31 self)
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Abstract. We provide a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.
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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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 fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can 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.
A sparse approximate inverse preconditioner for nonsymmetric linear systems
 SIAM J. SCI. COMPUT
, 1998
"... This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner f ..."
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Cited by 192 (22 self)
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This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner
A class of nonsymmetric preconditioners for saddle point problems
 Scientific Computing and Computational Mathematics, Stanford University, of Saddle Point Problems 77
, 2004
"... Abstract. For iterative solution of saddle point problems, a nonsymmetric preconditioning is studied which, with respect to the upperleft block of the system matrix, can be seen as a variant of SSOR. An idealized situation where the SSOR is taken with respect to the skewsymmetric part plus the dia ..."
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Cited by 3 (1 self)
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the diagonal part of the upperleft block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an innerouter iterative process. Numerical experiments with solution of linearized
ILU PRECONDITIONERS FOR NONSYMMETRIC SADDLE POINT MATRICES WITH APPLICATION TO THE INCOMPRESSIBLE
, 2015
"... ILU preconditioners for nonsymmetric saddle point matrices with application to the incompressible NavierStokes equations ..."
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ILU preconditioners for nonsymmetric saddle point matrices with application to the incompressible NavierStokes equations
A robust algebraic multilevel preconditioner for nonsymmetric Mmatrices
, 2000
"... Stable finite difference approximations of convection–diffusion equations lead to large sparse linear systems of equations whose coefficient matrix is an Mmatrix, which is highly nonsymmetric when the convection dominates. For an efficient iterative solution of such systems, it is proposed to cons ..."
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Cited by 8 (5 self)
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Stable finite difference approximations of convection–diffusion equations lead to large sparse linear systems of equations whose coefficient matrix is an Mmatrix, which is highly nonsymmetric when the convection dominates. For an efficient iterative solution of such systems, it is proposed
Parallel Inexact Constraint Preconditioners for Saddle Point Problems
"... Abstract. In this paper we propose a parallel implementation of the FSAI preconditioner to accelerate the PCG method in the solution of symmetric positive definite linear systems of very large size. This preconditioner is used as building block for the construction of an indefinite Inexact Constrain ..."
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Abstract. In this paper we propose a parallel implementation of the FSAI preconditioner to accelerate the PCG method in the solution of symmetric positive definite linear systems of very large size. This preconditioner is used as building block for the construction of an indefinite Inexact
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