The IBiCG method for large and sparse linear systems

210. L. T. Yang and R. P. Brent, The improved conjugate gradient squared (ICGS) method on parallel distributed memory architectures, Workshop Proceedings of the 2001 International Conference on Parallel Processing (ICPP-HPSECA01), Valencia, Spain, September 2001, 161-165.

ICPP paper: pdf (524K).


For the solution of large and sparse linear systems of equations with unsymmetric coefficient matrices, we propose an improved version of the Conjugate Gradient Squared (ICGS) method. An algorithm is derived with the properties that all inner products, matrix-vector multiplications, and vector updates of a single iteration step are independent, and the communication time required for inner products can be overlapped efficiently with the computation time of vector updates. Therefore, the cost of global communication on parallel distributed memory computers is significantly reduced. The resulting ICGS algorithm maintains the favourable properties of the original algorithm while not increasing computational costs. The efficiency of the ICGS algorithm is demonstrated by numerical experiments carried out on a massively parallel distributed memory system.

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