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A New Library for Parallel Algebraic Computation
, 1993
"... We give an overview on Paclib, a library for parallel algebraic computation on shared memory multiprocessors. Paclib is essentially a package of C functions that provide the basic objects and methods of computer algebra in a parallel context. The Paclib programming model supports concurrency, share ..."
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Cited by 11 (9 self)
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We give an overview on Paclib, a library for parallel algebraic computation on shared memory multiprocessors. Paclib is essentially a package of C functions that provide the basic objects and methods of computer algebra in a parallel context. The Paclib programming model supports concurrency, shared memory communication, nondeterminism and speculative parallelism. The system is based on a heap management kernel with parallelized garbage collection that is portable among most Unix machines. We present the successful application of paclib for the parallelization of several algebraic algorithms and discuss the achieved results. 1 Introduction Scientific computing is a rich source of challenging problems such as the solution of systems of partial differential equations. Classical numerical methods operate with efficient finiteprecision (floating point) arithmetic and thus quickly yield approximative solutions. However, often one is also interested in certain qualitative aspects like s...
The Exact Solution of Linear Equation Systems on a Shared Memory Multiprocessor
 In Submitted to the PARLE 93
, 1992
"... We describe the design of a parallel algorithm for the exact solution of linear equation systems with integer coefficients and the implementation of this algorithm on a shared memory multiprocessor. An efficient solution of the original problem is difficult since the coefficients grow during the com ..."
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Cited by 3 (3 self)
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We describe the design of a parallel algorithm for the exact solution of linear equation systems with integer coefficients and the implementation of this algorithm on a shared memory multiprocessor. An efficient solution of the original problem is difficult since the coefficients grow during the computation and arithmetic becomes very timeconsuming. Therefore we transform the problem into a problem of determinant computation and apply a modular approach: the system is mapped into several finite fields where the determinants can be efficiently computed. The subresults are combined to yield the original determinants and to compute the solutions of the system. Several parallel versions of this algorithm have been developed and implemented on a shared memory multiprocessor. The programs are applied to equation systems of different characteristics and the results are analyzed and compared. Keywords: Parallel algorithms, scientific computing, computer algebra, shared memory machines. Fund...
Solving Systems of Linear Equations Functionally: a Case Study in Parallelisation
, 1995
"... This paper describes the development of a parallel, functional algorithm for a realworld computer algebra problem: solving a system of linear equations. The program was developed using our GranSim simulator for parallel Haskell, which is based on the Glasgow Haskell Compiler. We provide concrete si ..."
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Cited by 2 (2 self)
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This paper describes the development of a parallel, functional algorithm for a realworld computer algebra problem: solving a system of linear equations. The program was developed using our GranSim simulator for parallel Haskell, which is based on the Glasgow Haskell Compiler. We provide concrete simulation results for a variety of machine architectures characterised by differences in communications latency. These demonstrate absolute speedups over the sequential algorithm of 20.12 for 32 processors on a tightlycoupled distributedmemory machine, similar to our GRIP multiprocessor. Comparisons are also given with the same program executed on the physical GRIP machine, and with a previously produced imperative version. While the functional program exploits parallelism better (and so is more scalable), absolute performance is (sadly) still better for the imperative program. 1 Introduction In the imperative world, novel algorithms are often embedded into special purpose solutions for s...