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  • 1
    Electronic Resource
    Electronic Resource
    MCGS: A Modified Conjugate Gradient Squared Algorithm for Nonsymmetric Linear Systems (1999)
    Springer
    The journal of supercomputing 14 (1999), S. 257-280 
    Details
    ISSN: 1573-0484
    Keywords: algorithm scalability ; conjugate gradient squared ; modified conjugate gradient squared ; Intel Paragon ; IBM SP-2 ; MIMD ; synchronization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The conjugate gradient squared (CGS) algorithm is a Krylov subspace algorithm that can be used to obtain fast solutions for linear systems (Ax=b) with complex nonsymmetric, very large, and very sparse coefficient matrices (A). By considering electromagnetic scattering problems as examples, a study of the performance and scalability of this algorithm on two MIMD machines is presented. A modified CGS (MCGS) algorithm, where the synchronization overhead is effectively reduced by a factor of two, is proposed in this paper. This is achieved by changing the computation sequence in the CGS algorithm. Both experimental and theoretical analyses are performed to investigate the impact of this modification on the overall execution time. From the theoretical and experimental analysis it is found that CGS is faster than MCGS for smaller number of processors and MCGS outperforms CGS as the number of processors increases. Based on this observation, a set of algorithms approach is proposed, where either CGS or MGS is selected depending on the values of the dimension of the A matrix (N) and number of processors (P). The set approach provides an algorithm that is more scalable than either the CGS or MCGS algorithms. The experiments performed on a 128-processor mesh Intel Paragon and on a 16-processor IBM SP2 with multistage network indicate that MCGS is approximately 20% faster than CGS.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008141600003
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  • 2
    Electronic Resource
    Electronic Resource
    Parallel Image Correlation: Case Study to Examine Trade-Offs in Algorithm-to-Machine Mappings (1998)
    Springer
    The journal of supercomputing 12 (1998), S. 7-35 
    Details
    ISSN: 1573-0484
    Keywords: image correlation ; Intel Paragon ; MasPar MP-1 ; MIMD ; mixed-mode ; nCUBE 2 ; PASM prototype ; scalability ; SIMD
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Performance of a parallel algorithm on a parallel machine depends not only on the time complexity of the algorithm, but also on how the underlying machine supports the fundamental operations used by the algorithm. This study analyzes various mappings of image correlation algorithms in SIMD, MIMD, and mixed-mode environments. Experiments were conducted on the Intel Paragon, MasPar MP-1, nCUBE 2, and PASM prototype. The machine features considered in this study include: modes of parallelism, communication/computation ratio, network topology and implementation, SIMD CU/PE overlap, and communication/computation overlap. Performance of an implementation can be enhanced by using algorithmic techniques that match the machine features. Some algorithmic techniques discussed here are additional communication versus redundant computation, data block transfers, and communication/computation overlap. The results presented are applicable to a large class of image processing tasks. Case studies, such as the one presented here, are a necessary step in developing software tools for mapping an application task onto a single parallel machine and for mapping the subtasks of an application task, or a set of independent application tasks, onto a heterogeneous suite of parallel machines.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007973225694
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