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The Conjugate Gradient method involves one matrix-vector product, three
vector updates, and two inner products per iteration. Some slight
computational variants exist that have the same
structure (see Reid [174]). Variants that cluster the inner products, a favorable property on
parallel machines, are discussed in §
.
For a discussion of the Conjugate Gradient method on vector and shared
memory computers, see Dongarra, et
al. [162][68]. For discussions
of the method for more general parallel architectures
see Demmel, Heath and Van der Vorst [64] and
Ortega [162], and the references therein.