Minimizing Residuals

1 J Minimizing Residuals. When the purchase of paint in bulk containers is not practical, then paint should be purchased in the smallest amount required so as to minimize the amount of residual. Workers should not open a one gallon can of paint when only a quart or two are required. While the per unit cost of paint when purchased in various small quantity containers is greater than the cost of paint when purchased in larger quantities, the savings in reduced paint wastage and disposal costs could still be substantial. 

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Solvent recovery is fast and complete, with minimal residue in product. Properties of GO2 as a solvent ... 

Residual stresses caused by large temperature differences between the weld bead and adjacent metal can be reduced by preheating the metals to be welded, especially if the sections are thick, or by stress-relief-annealing following the welding procedure. Proper welding techniques, especially the use of appropriate weld filler metals to minimize weld-metal shrinkage, can minimize residual stresses. 

We confine ourselves here to the minimal residual method and the method of steepest descent relating to two-layer schemes. As usual, the explicit scheme is considered first ... 

The only difference between the methods we have mentioned above lies in the selection rules for the parameter In the minimal residual... 

Tj, 2/(7i -b 72), thereby justifying estimate (17) and the convergence of the minimal residual method with the same rate as occurred before for the simple iteration method with the exact values 71 and... 

The implicit minimal residual method can be designed in line with established practice ... 

Applying here the explicit minimal residual method yields... 

No doubt, several conclusions can be drawn from such reasoning. First, the method being employed above converges in the space Ha with the same rate as the simple iteration method although it occurs in one of the subordinate norms. Second, the minimal residual method converges in the space Ha, that is, in a more stronger norm. 

The minimal residual method can be employed for the equation Au = / with a non-self-adjoint operator A, the convergence rate of which coincides with that of scheme (30) for r = f. 

This is certainly true for the minimal residual method (13)-(14) under conditions (34). Here is a solution of problem (13) and p is specified by... 

In the production of crude oil, the greatest part of the crude oil occurs as a water-in-oil emulsion. The composition of the continuous phase depends on the water/oil ratio, the natural emulsifier systems contained in the oil, and the origin of the emulsion. The natural emulsifiers contained in crude oils have a complex chemical structure, so that, to overcome their effect, petroleum-emulsion demulsifiers must be selectively developed. As new oil fields are developed, and as the production conditions change at older fields, there is a constant need for demulsifiers that lead to a rapid separation into water and oil, as well as minimal-residual water and salt mixtures. 

C followed by formation of aromatic hydrocarbons. Minimal residue could be obtained overMO catalysts (Fe,Mg,Al-MO and Ca,Mg,Al-MO). 

CBT (exposure therapy, cognitive restructuring, relaxation training, and social skills training) and pharmacotherapy are considered equally effective in SAD, but CBT can lead to a greater likelihood of maintaining response after treatment termination. Even after response, most patients continue to experience more than minimal residual symptoms. 

Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. 

H. O. Karlsson,/. Chem. Phys., 103, 4914 (1995). The Quasi-Minimal Residual Algorithm... 

Some people have a good 3 dimensional imagination. They immediately see that the closest point on the plane is just vertically underneath the tip of the vector y. Using more appropriate expressions the minimal residual vector r, which is the shortest difference between y and Fa, is orthogonal, or normal, to the plane defined by F. 

The applicability of Eq. (45) to a broad range of biological (i.e., toxic, geno-toxic) structure-activity relationships has been demonstrated convincingly by Hansch and associates and many others in the years since 1964 [60-62, 80, 120-122, 160, 161, 195, 204-208, 281-285, 289, 296-298]. The success of this model led to its generalization to include additional parameters in attempts to minimize residual variance in such correlations, a wide variety of physicochemical parameters and properties, structural and topological features, molecular orbital indices, and for constant but for theoretically unaccountable features, indicator or dummy variables (1 or 0) have been employed. A widespread use of Eq. (45) has provided an important stimulus for the review and extension of established scales of substituent effects, and even for the development of new ones. It should be cautioned here, however, that the general validity or indeed the need for these latter scales has not been established. 

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