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Numerical solution of saddle point problems
 ACTA NUMERICA
, 2005
"... Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has b ..."
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Cited by 322 (25 self)
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been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for solving this type of systems. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods
Convergent Treereweighted Message Passing for Energy Minimization
 ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI)
, 2006
"... Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
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Cited by 489 (16 self)
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Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 436 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
Complements on Hilbert Spaces and Saddle Point Systems
 Journal of Computational and Applied Mathematics, Volume 225, Issue
"... For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility LadyshenskayaBabušcaBrezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators onl ..."
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Cited by 8 (8 self)
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symmetric saddle point problem, the inexact Uzawa algorithm converges provided that the inexact process for inverting the residual at each step has the relative error smaller than 1/3. As a consequence, we provide a new type of algorithm for discretizing saddle point problems, which combines the inexact
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
 SIAM J. Numer. Anal
, 1997
"... . In this paper, we consider the socalled "inexact Uzawa" algorithm for iteratively solving block saddle point problems. Such saddle point problems arise, for example, in finite element and finite difference discretizations of Stokes equations, the equations of elasticity and mixed finite ..."
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Cited by 93 (4 self)
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. In this paper, we consider the socalled "inexact Uzawa" algorithm for iteratively solving block saddle point problems. Such saddle point problems arise, for example, in finite element and finite difference discretizations of Stokes equations, the equations of elasticity and mixed
Regularization and stabilization of discrete saddlepoint variational problems
 Electronic Transactions on Numerical Analysis
"... Abstract. Our paper considers parameterized families of saddlepoint systems arising in the nite element solution of PDEs. Such saddle point systems are ubiquitous in science and engineering. Our motivation is to explain how these saddlepoint systems can be modied to avoid onerous stability conditi ..."
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Cited by 3 (1 self)
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Abstract. Our paper considers parameterized families of saddlepoint systems arising in the nite element solution of PDEs. Such saddle point systems are ubiquitous in science and engineering. Our motivation is to explain how these saddlepoint systems can be modied to avoid onerous stability
Preconditioning stochastic Galerkin saddle point systems
 SIAM J. MATRIX ANAL. APPL
, 2009
"... Mixed finite element discretizations of deterministic secondorder elliptic partial differential equations (PDEs) lead to saddle point systems for which the study of iterative solvers and preconditioners is mature. Galerkin approximation of solutions of stochastic secondorder elliptic PDEs, which ..."
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Cited by 110 (4 self)
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, which couple standard mixed finite element discretizations in physical space with global polynomial approximation on a probability space, also give rise to linear systems with familiar saddle point structure. For stochastically nonlinear problems, the solution of such systems presents a serious
Pyramidal implementation of the Lucas Kanade feature tracker
 Intel Corporation, Microprocessor Research Labs
, 2000
"... grayscale value of the two images are the location x = [x y] T, where x and y are the two pixel coordinates of a generic image point x. The image I will sometimes be referenced as the first image, and the image J as the second image. For practical issues, the images I and J are discret function (or ..."
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Cited by 308 (0 self)
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grayscale value of the two images are the location x = [x y] T, where x and y are the two pixel coordinates of a generic image point x. The image I will sometimes be referenced as the first image, and the image J as the second image. For practical issues, the images I and J are discret function (or
Analysis of Preconditioners for SaddlePoint Problems
"... Contents 1 Introduction 3 2 Preliminaries 4 2.1 De nitions and standard results . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Norm and eldofvalues equivalence . . . . . . . . . . . . . . . . . . . . . 7 2.3 Normequivalent preconditioners . . . . . . . . . . . . . . . . . . . . . . . . ..."
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Cited by 13 (5 self)
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. . . . . . . . . . . . . . . . . . . . . . . . 8 3 Saddlepoint preconditioners 10 3.1 Some useful results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Normequivalent preconditioners . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Applications 17 4.1 Example: NavierStokes ow
THE DISCRETE GEODESIC PROBLEM
, 1987
"... We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and ..."
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Cited by 180 (1 self)
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path from the source to a destination can be reported in time O(k+log n), where k is the number of faces crossed by the path. The algorithm generalizes to the case of multiple source points to build the Voronoi diagram on the surface, where n is now the maximum of the number of vertices and the number
Results 1  10
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