Discretisation of sparse linear systems: An optimisation approach

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

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Efficient solution of large sparse linear systems in modern hardware

2015 6th International Conference on Information, Intelligence, Systems and Applications (IISA) ◽

10.1109/iisa.2015.7388040 ◽

2015 ◽

Cited By ~ 1

Author(s):

Athanasios Fevgas ◽

Konstantis Daloukas ◽

Panagiota Tsompanopoulou ◽

Panayiotis Bozanis

Keyword(s):

Linear Systems ◽

Efficient Solution ◽

Sparse Linear Systems

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A compact and modular VLSI design for the solution of general sparse linear systems

Integration ◽

10.1016/s0167-9260(87)80007-x ◽

1987 ◽

Vol 5 (1) ◽

pp. 77-86 ◽

Cited By ~ 3

Author(s):

B. Codenotti ◽

F. Romani

Keyword(s):

Linear Systems ◽

Vlsi Design ◽

Sparse Linear Systems

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MRILDU: An Improvement to ILUT Based on Incomplete LDU Factorization and Dropping in Multiple Rows

Journal of Applied Mathematics ◽

10.1155/2014/467672 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Jian-Ping Wu ◽

Huai-Fa Ma

Keyword(s):

Computational Complexity ◽

Linear Systems ◽

Numerical Weather Prediction ◽

Sparse Matrix ◽

Weather Prediction ◽

Concrete Sample ◽

Storage Requirement ◽

Sparse Linear Systems ◽

Numerical Weather ◽

Do So

We provide an improvement MRILDU to ILUT for general sparse linear systems in the paper. The improvement is based on the consideration that relatively large elements should be kept down as much as possible. To do so, two schemes are used. Firstly, incomplete LDU factorization is used instead of incomplete LU. Besides, multiple rows are computed at a time, and then dropping is applied to these rows to extract the relatively large elements in magnitude. Incomplete LDU is not only fairer when there are large differences between the elements of factorsLandU, but also more natural for the latter dropping in multiple rows. And the dropping in multiple rows is more profitable, for there may be large differences between elements in different rows in each factor. The provided MRILDU is comparable to ILUT in storage requirement and computational complexity. And the experiments for spare linear systems from UF Sparse Matrix Collection, inertial constrained fusion simulation, numerical weather prediction, and concrete sample simulation show that it is more effective than ILUT in most cases and is not as sensitive as ILUT to the parameterp, the maximum number of nonzeros allowed in each row of a factor.

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