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Sparse matrix representations in a functional language

  • P. W. Grant (a1), J. A. Sharp (a1), M. F. Webster (a1) and X. Zhang (a1)

This paper investigates several sparse matrix representation schemes and associated algorithms in Haskell for solving linear systems of equations arising from solving realistic computational fluid dynamics problems using a finite element algorithm. This work complements that of Wainwright and Sexton (1992) in that a Choleski direct solver (with an emphasis on its forward/backward substitution steps) is examined. Experimental evidence comparing time and space efficiency of these matrix representation schemes is reported, together with associated forward/backward substitution implementations. Our results are in general agreement with Wainwright and Sexton's.

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C. Cuvelier , A. Segal and A. A. van Steenhoven (1986) Finite Element Methods and Navier-Stokes Equations. Reidel Publishing Co.

D. Ding , P. Townsend and M. F. Webster (1993) Computer modelling of transient thermal flows of non-Newtonian fluids. J. Non-Newtonian Fluid Mechanism, 47: 239–56.

P. W. Grant , J. A. Sharp , M. F. Webster and X. Zhang (1993b) Some issues in a functional implementation of a finite element algorithm. In Proc. FPCA '93, pp. 1217. Copenhagen, Denmark, June. ACM SIGPLAN/SIGARCH.

L. A. Hageman and D. M. Young (1981) Applied Iterative Methods. Academic Press.

D. M. Hawken , H. R. Tamaddon-Jahromi , P. Townsend and M. F. Webster (1990) A Taylor-Galerkin-based algorithm for viscous incompressible flow. Int. J. Num. Meth. Fluids, 10: 327351.

P. Hudak , S. L. Peyton Jones and P. Wadler , editors (1992) Report on the Programming Language Haskell, A Non-strict Purely Functional Language (Version 1.2). SIGPLAN Notices, May.

J. W. H. Liu (1986) A compact row storage scheme for Choleski factors using elimination trees. ACM Trans. Math. Software, 12: 127148. June.

J. W. H. Liu (1991) A generalized envelope method for sparse factorization by rows. ACM Trans. Math. Software, 17: 112129. March.

M. Spivey (1990) A functional theory of exceptions. Science of Computer Programming, 14(1): 2542. June.

J. H. Wilkinson and C. Reinsch (1971) Handbook for Automatic Computation, Linear Algebra, vol. II. Springer-Verlag.

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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
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