The IBiCG method for large and sparse linear systems
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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