A Combinatorial Scheme for Developing Efficient Composite Solvers

  • Sanjukta Bhowmick
  • Padma Raghavan
  • Keita Teranishi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2330)


Many fundamental problems in scientific computing have more than one solution method. It is not uncommon for alternative solution methods to represent different tradeoffs between solution cost and reliability. Furthermore, the performance of a solution method often depends on the numerical properties of the problem instance and thus can vary dramatically across application domains. In such situations, it is natural to consider the construction of a multi-method composite solver to potentially improve both the average performance and reliability. In this paper, we provide a combinatorial framework for developing such composite solvers. We provide analytical results for obtaining an optimal composite from a set of methods with normalized measures of performance and reliability. Our empirical results demonstrate the effectiveness of such optimal composites for solving large, sparse linear systems of equations.


Execution Time Short Path Combinatorial Scheme Total Execution Time Utility Ratio 
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  1. 1.
    Barrett, R., Berry, M., Dongarra, J., Eijkhout, V., Romine, C.: Algorithmic Bombardment for the Iterative Solution of Linear Systems: A PolyIterative Approach. Journal of Computational and applied Mathematics, 74, (1996) 91–110zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bramley, R., Gannon, D., Stuckey, T., Villacis, J., Balasubramanian, J., Akman, E., Berg, F., Diwan, S., Govindaraju, M.:Component Architectures for Distributed Scientific Problem Solving. To appear in a special issue of IEEE Computational Science and Eng., 2001Google Scholar
  3. 3.
    Golub, G.H., Van Loan, C.F.: Matrix Computations (3rd Edition). The John Hopkins University Press, Baltimore Maryland (1996)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Sanjukta Bhowmick
    • 1
  • Padma Raghavan
    • 1
  • Keita Teranishi
    • 1
  1. 1.Department of Computer Science and EngineeringThe Pennsylvania State University

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