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We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi Davidson algorithm, very efficiently in parallel.

Pretreatment is considered the most costly step in the conversion of biomass to bioethanol [ 9- 13].

In many cases the regeneration step is the most costly step of the entire process [ 21].

For industrial applications, the removal of the affinity tag by endoproteases is the most costly step in protein production, and can interfere with the biological activity of the purified component (Wood et al. 2005).

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Dewatering process is one of the most costly steps in mineral processing and coal washing plants.

Enzymatic hydrolysis of cellulose is one of the most costly steps in the bioconversion of lignocellulosic biomass.

In addition, the pre-treatment process to remove lignin is one the most costly steps of cellulosic ethanol production [ 61- 64].

Hence, pretreatment still remains one of the most costly steps in cellulosic H2 production and is a significant barrier to commercialization of biohydrogen production from lignocellulosic biomass.

One of the most costly steps in this process is the fluorescent labeling of individual microsatellite primers, with costs varying depending upon the dye used (e.g., 6-FAM, VIC, NED) and the manufacturer.

As a result, the complexity of the MLE is determined by the most costly computation step that is the matrix inversion O (N 3).

In Japan's case, some of the most costly and wrenching steps were yet to come.

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