CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Krylov subspace methods on supercomputers
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Highly parallel computing (2nd ed.)
Highly parallel computing (2nd ed.)
Multiple quadratic forms: a case study in the design of data-parallel algorithms
Journal of Parallel and Distributed Computing - Special issue on data parallel algorithms and programming
IBM Systems Journal
The SP2 high-performance switch
IBM Systems Journal
Early prediction of MPP performance: the SP2, T3D, and Paragon experiences
Parallel Computing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Modeling Communication Overhead: MPI and MPL Performance on the IBM SP2
IEEE Parallel & Distributed Technology: Systems & Technology
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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.