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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 275 (24 self)
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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 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 for large and sparse problems.
Stability of the diagonal pivoting method with partial pivoting
 SIAM J. Matrix Anal. Appl
, 1995
"... Abstract. LAPACK and LINPACK both solve symmetric indefinite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman [Math. Comp., 31 (1977), pp. 163–179]. No proof of the stability of this method has appeared in the literature. It is tempting to arg ..."
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Cited by 26 (9 self)
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Abstract. LAPACK and LINPACK both solve symmetric indefinite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman [Math. Comp., 31 (1977), pp. 163–179]. No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small. We show that this argument is false in general and give a sufficient condition for stability. This condition is not satisfied by the partial pivoting strategy because the multipliers are unbounded. Nevertheless, using a more specific approach we are able to prove the stability of partial pivoting, thereby filling a gap in the body of theory supporting LAPACK and LINPACK.
Techniques in Computational Stochastic Dynamic Programming
 in Control and Dynamic Systems
, 1996
"... INTRODUCTION When Bellman introduced dynamic programming in his original monograph [8], computers were not as powerful as current personal computers. Hence, his description of the extreme computational demands as the Curse of Dimensionality [9] would not have had the super and massively parallel p ..."
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Cited by 12 (8 self)
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INTRODUCTION When Bellman introduced dynamic programming in his original monograph [8], computers were not as powerful as current personal computers. Hence, his description of the extreme computational demands as the Curse of Dimensionality [9] would not have had the super and massively parallel processors of today in mind. However, massive and super computers can not overcome the Curse of Dimensionality alone, but parallel and vector computation can permit the solution of higher dimension than was previously possible and thus permit more realistic dynamic programming applications. Today such large problems are called Grand and National Challenge problems [45, 46] in high performance computing. Today's availability of high performance vector supercomputers and massively parallel processors have made it possible to compute optimal policies and values of control systems for much larger dimensions than was possible earlier. Advance
Numerical Analysis
, 1989
"... Introduction. Numerical anC"Cfix is the area of mathematics a n computerscienB that creates, a n lyzes, a n implemen ts algorithms for solvin n umerically the problems of con tin uous mathematics. Such problems origi n te genfi ally from realworld application s of algebra, geometryan d calculu ..."
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Cited by 3 (0 self)
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Introduction. Numerical anC"Cfix is the area of mathematics a n computerscienB that creates, a n lyzes, a n implemen ts algorithms for solvin n umerically the problems of con tin uous mathematics. Such problems origi n te genfi ally from realworld application s of algebra, geometryan d calculus,an d they in volve variables which vary con tin uously; these problems occur throughout the n tural scienfiB( social scien(Ifi e n infiC in , medicinI a n businB(I Durin the past halfcen tury, the growthin power a n availability of digital computers has led to an inE easin use of realistic mathematical models in scien cean d en gin eerin g,an dn umericalan alysis of infifiBBE(I sophistication has been nnAC to solve these more detailed mathematical models of the world. The formal academic area ofn umerical an alysis varies from quite theoretical mathematical studies (e.g. see [5]) to computer scienr issues (e.g. see [1], [11]). With the growth in importa n( of usin computers to carry outn umeri
Analyzing Data Structures for Parallel Sparse Direct Solvers: Pivoting And FillIn
 TO 168, PROCEEDINGS OF THE SIXTH WORKSHOP ON COMPILERS FOR PARALLEL COMPUTERS, CPC'96, SPECIAL ISSUE OF THE VOLUME KONFERENZEN DES FORSCHUNGSZENTRUMS JULICH, VOL.21
, 1996
"... This paper addresses the problem of the parallelization of sparse direct methods for the solution of linear systems in distributed memory multiprocessors. Sparse direct solvers include pivoting operations and suffer from fillin, problems that turn the efficient parallelization into a challenging ..."
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Cited by 2 (2 self)
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This paper addresses the problem of the parallelization of sparse direct methods for the solution of linear systems in distributed memory multiprocessors. Sparse direct solvers include pivoting operations and suffer from fillin, problems that turn the efficient parallelization into a challenging task. We present some data structures to store the sparse matrices that permit to deal in a efficient way with both problems. These data structures have been evaluated on a Cray T3D, implementing, in particular, LU and QR factorizations as examples of direct solvers. Any of the data representations considered enforces the handling of indirections for data accesses, pointer referencing and dynamic data creation. All of
ANALYSIS AND SUPPRESSION OF INSTABILITIES IN VISCOELASTIC FLOWS By
, 2001
"... The viscoelastic character of polymer solutions and melts gives rise to instabilities that are not seen in the flows of Newtonian liquids. In industrial applications such as coating and extrusion, these socalled “elastic ” instabilities can impose a limitation on the throughput. Hence, it is import ..."
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The viscoelastic character of polymer solutions and melts gives rise to instabilities that are not seen in the flows of Newtonian liquids. In industrial applications such as coating and extrusion, these socalled “elastic ” instabilities can impose a limitation on the throughput. Hence, it is important to understand, and if possible, to suppress them. The first instability we study is the phenomenon of melt fracture, which occurs in the extrusion of polymer melts and takes the form of gross distortions of the surface of the extrudate. This instability is linked to the phenomenon of wallslip, i.e., the velocity of the polymer at the wall relative to the velocity of the wall itself (also called the slip velocity) is nonzero. Several slip relations based on microscopic theories for polymers predict regions in which the slip velocity is multivalued. The expectation is that a multivalued slip relation will result in a multivalued flow curve, which in turn causes melt fracture. Using a simple slip relation, we show that when the dependence of the slip velocity on the pressure is taken into account, this is not necessarily true: a multivalued slip law does not necessarily imply a multivalued flow curve. The second instability we study is the “filament stretching instability, ” which occurs
CIRJEF478 On the estimation of a large sparse Bayesian system: the Snaer program
, 2007
"... CIRJE Discussion Papers can be downloaded without charge from: ..."
Persistent InterIndustry Wage Differences: Rent
, 2005
"... developed the computational algorithms used in this paper. They also acknowledge funding from the NSF (SBER 9618111 to the NBER and SES 9978093 to Cornell University). Joe Altonji, Orley ..."
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developed the computational algorithms used in this paper. They also acknowledge funding from the NSF (SBER 9618111 to the NBER and SES 9978093 to Cornell University). Joe Altonji, Orley
1Algebraic MultiColor Ordering Method for Parallelized ICCG Solver in Unstructured Finite Element Analyses
"... Abstract — The present paper proposes a new blackbox type parallelized ICCG solver. The new method is based on a multicolor ordering concept and an automatic reordering process in the solver. Parallel performance is evaluated in the context of 3D finite edgeelement eddycurrent analysis. The pr ..."
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Abstract — The present paper proposes a new blackbox type parallelized ICCG solver. The new method is based on a multicolor ordering concept and an automatic reordering process in the solver. Parallel performance is evaluated in the context of 3D finite edgeelement eddycurrent analysis. The proposed method attains high parallelism with a small increase in iterations and achieves high parallel performance. I.