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13
The Design of a New Frontal Code for Solving Sparse Unsymmetric Systems
, 1996
"... We describe the design, implementation, and performance of a frontal code for the solution of large sparse unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is intended to supersede the earlier MA32 package. ..."
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Cited by 35 (17 self)
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We describe the design, implementation, and performance of a frontal code for the solution of large sparse unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is intended to supersede the earlier MA32 package. We discuss in detail the extensive use of higher level BLAS kernels within MA42 and illustrate the performance on a range of practical problems on a CRAY YMP, an IBM 3090, and an IBM RISC System/6000. We examine extending the frontal solution scheme to use multiple fronts to allow MA42 to be run in parallel. We indicate some directions for future development. Keywords : sparse unsymmetric linear equations, unsymmetric frontal method, Gaussian elimination, finiteelement equations, level 3 BLAS, parallel processing. AMS(MOS) subject classification : 65F05, 65F50. CR classification system : G.1.3. Computing and Information Systems Department, Atlas Centre, Rutherford Appleton Laborator...
Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier Stokes equations.
 SIAM J. Matrix Anal. Appl
, 1997
"... We are concerned with finding a few eigenvalues of the large sparse nonsymmetric generalized eigenvalue problem Ax = Bx that arises in stability studies of incompressible fluid flow. The matrices have a block structure that is typical of mixed finiteelement discretizations for such problems. We ..."
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Cited by 22 (3 self)
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We are concerned with finding a few eigenvalues of the large sparse nonsymmetric generalized eigenvalue problem Ax = Bx that arises in stability studies of incompressible fluid flow. The matrices have a block structure that is typical of mixed finiteelement discretizations for such problems. We examine the use of shiftinvert and Cayley transformations in conjunction with the implicitly restarted Arnoldi method along with using a semiinner product induced by B and purification techniques. Numerical results are presented for some model problems arising from the ENTWIFE finiteelement package. Our conclusion is that, with careful implementation, implicitly restarted Arnoldi methods are reliable for linear stability analysis. AMS classification: Primary 65F15; Secondary 65F50 Key Words: eigenvalues, sparse nonsymmetric matrices, Arnoldi's method. 1 Introduction Mixed finiteelement discretizations of timedependent equations modelling incompressible fluid flow problems ty...
The use of multiple fronts in Gaussian elimination
 in Gaussian Elimination, Proc. Fifth SIAM Conf. on Applied Linear Algebra, SIAM
, 1994
"... We examine a method for extending a frontal solution scheme principally so that parallelism can be exploited in the solution process. We see also that this technique can reduce the amount of work required and enable the solution of very large problems even on uniprocessors. Keywords: sparse matrice ..."
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Cited by 17 (9 self)
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We examine a method for extending a frontal solution scheme principally so that parallelism can be exploited in the solution process. We see also that this technique can reduce the amount of work required and enable the solution of very large problems even on uniprocessors. Keywords: sparse matrices, frontal methods, parallel processing, PVM, domain decomposition. AMS(MOS) subject classifications: 65F05, 65F50. 1 Extended and revised version of paper in Proceedings of the Fifth SIAM Conference on Applied Linear Algebra. Edited by John Lewis. SIAM Press, 567571. 2 Current reports available by anonymous ftp from camelot.cc.rl.ac.uk (internet 130.246.8.61) in the directory "pub/reports". This report is in file dsRAL94040.ps.Z. Central Computing Department Atlas Centre Rutherford Appleton Laboratory Oxon OX11 0QX September 13, 1994. Contents 1 Introduction 1 2 Frontal schemes 1 3 The use of multiple fronts 3 4 The use of MA42 for multiple front algorithms 4 4.1 MA42 code : :...
MA42  A new frontal code for solving sparse unsymmetric systems
, 1993
"... We describe the design, implementation, and performance of a frontal code for the solution of large sparse unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is intended to supersede the earlier MA32 package. ..."
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Cited by 10 (8 self)
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We describe the design, implementation, and performance of a frontal code for the solution of large sparse unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is intended to supersede the earlier MA32 package. We discuss in detail design changes from the earlier code, indicating the way in which they aid clarity, maintainability, and portability. The new design also permits extensive use of higher level BLAS kernels, which aid both modularity and efficiency. We illustrate the performance of our new code on practical problems on a CRAY YMP, an IBM 3090, and an IBM RISC System/6000. We indicate some directions for future development.
MA57  A new code for the solution of sparse Symmetric Definite And indefinite Systems
, 2002
"... We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe the user interface in some detail and emphasize some o ..."
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Cited by 10 (1 self)
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We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe the user interface in some detail and emphasize some of the novel features of MA57. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple righthand sides, and iterative refinement and error analysis. There are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications and the performance of the code on problems arising therefrom will be presented.
Performance Issues for Frontal Schemes on a CacheBased High Performance Computer
, 1997
"... We consider the implementation of a frontal code for the solution of large sparse unsymmetric linear systems on a high performance computer where data must be in the cache before arithmetic operations can be performed on it. In particular, we show how we can modify the frontal solution algorithm to ..."
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Cited by 8 (7 self)
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We consider the implementation of a frontal code for the solution of large sparse unsymmetric linear systems on a high performance computer where data must be in the cache before arithmetic operations can be performed on it. In particular, we show how we can modify the frontal solution algorithm to enhance the proportion of arithmetic operations performed using Level 3 BLAS thus enabling better reuse of data in the cache. We illustrate the effects of this on Silicon Graphics Power Challenge machines using problems which arise in real engineering and industrial applications. Keywords: unsymmetric sparse matrices, frontal solver, direct methods, finiteelements, BLAS, computational kernels. AMS(MOS) subject classifications: 65F05, 65F50. 1 Current reports available by anonymous ftp from matisa.cc.rl.ac.uk in the directory pub/reports. This report is in file cdsRAL97001.ps.gz. 2 Address: AEA Technology, Harwell, Didcot, Oxon OX11 0RA, England. Department for Computation and Informa...
A Comparison of Frontal Software With Other Sparse Direct Solvers
, 1996
"... We compare the performance of sparse frontal codes from the Harwell Subroutine Library (HSL) against other HSL sparse direct solvers and consider the effect of ordering on the frontal solver. We study both the case of assembled and unassembled systems for both symmetric positivedefinite and unsymme ..."
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Cited by 8 (6 self)
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We compare the performance of sparse frontal codes from the Harwell Subroutine Library (HSL) against other HSL sparse direct solvers and consider the effect of ordering on the frontal solver. We study both the case of assembled and unassembled systems for both symmetric positivedefinite and unsymmetric matrices. We use problems arising in real engineering or industrial applications in our tests.
On the Use of ElementbyElement Preconditioners to Solve Large Scale Partially Separable Optimization Problems
"... We study the solution of largescale nonlinear optimization problems by methods which aim to exploit their inherent structure. In particular, we consider the allpervasive property of partial separability, first studied by Griewank and Toint (1982b). A typical minimizationmethod for nonlinear optimi ..."
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Cited by 8 (5 self)
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We study the solution of largescale nonlinear optimization problems by methods which aim to exploit their inherent structure. In particular, we consider the allpervasive property of partial separability, first studied by Griewank and Toint (1982b). A typical minimizationmethod for nonlinear optimization problems approximately solves a sequence of simplified linearized subproblems. In this paper, we explore how partial separability may be exploited by iterative methods for solving these subproblems. We particularly address the issue of computing effective preconditioners for such iterative methods. Numerical experiments indicate the effectiveness of these preconditioners on largescale examples. Keywords: largescale problems, unconstrained optimization, elememtbyelement preconditioners, conjugategradients. AMS(MOS) subject classifications: 65F05, 65F10, 65F15, 65F50, 65K05, 90C30. Also appeared as ENSEEIHTIRIT report RT/APO/94/4. 1 Travel was funded, in part, by the ALLIANCE...
Combinatorial problems in solving linear systems
, 2009
"... Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these two seemingly disparate subjects ..."
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Cited by 5 (3 self)
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Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these two seemingly disparate subjects. As the core of many of today’s numerical linear algebra computations consists of the solution of sparse linear system by direct or iterative methods, we survey some combinatorial problems, ideas, and algorithms relating to these computations. On the direct methods side, we discuss issues such as matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers. On the iterative method side, we discuss preconditioning techniques including incomplete factorization preconditioners, support graph preconditioners, and algebraic multigrid. In a separate part, we discuss the block triangular form of sparse matrices.
Direct Methods
, 1998
"... We review current methods for the direct solution of sparse linear equations. We discuss basic concepts such as fillin, sparsity orderings, indirect addressing and compare general sparse codes with codes for dense systems. We examine methods for greatly increasing the efficiency when the matrix is ..."
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Cited by 4 (0 self)
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We review current methods for the direct solution of sparse linear equations. We discuss basic concepts such as fillin, sparsity orderings, indirect addressing and compare general sparse codes with codes for dense systems. We examine methods for greatly increasing the efficiency when the matrix is symmetric positive definite. We consider frontal and multifrontal methods emphasizing how they can take advantage of vectorization, RISC architectures, and parallelism. Some comparisons are made with other techniques and the availability of software for the direct solution of sparse equations is discussed.