Ordering of the iterative parameters in the cyclical Chebyshev iterative method

Lebedev, V. I.; Finogenov, S. A.

doi:10.1016/0041-5553(71)90169-8

Cited by 35 publications

(32 citation statements)

References 3 publications

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“…After receiving ethanol or caffeine, the times taken by these runners to complete 1000 m were longer than those recorded in preliminary runs (before which they had received no treatment), and considerably longer than the times recorded after receiving S. chinensis or amphetamine. In corroboration of these positive responses, Lebedev (1967Lebedev ( , 1971 reported that schizandrin (6: an active component of S. chinensis) increased the working capacities of 20 year-old runners performing over a distance of 3000 m such that their running times were remarkably shorter than those of a control group that had been treated with placebo (glucose). In all doses tested, the stimulating effect of 6 was of the same order of magnitude as that of phenamine.…”

Section: Effect Of Adaptogens On Physical Working Capacitymentioning

confidence: 76%

“…Such pharmacologically active compounds were given the name "adaptogens" (Lasarev, 1962). As originally defined, an adaptogen was a substance that: (a) showed some 6 repeated doses (Lebedev, 1971;Lapajev, 1978;Lupandin and Lapajev, 1981;Panossian et al, 1997;ESCOP Monographs, 2003a, b;Saratikov and Krasnov, 2004). It soon became clear, however, that there were very important differences between the stimulating effects of adaptogens and those of other stimulants of the CNS and these are summarised in Table 2 ( Fulder, 1980) .…”

Section: Introductionmentioning

confidence: 99%

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Stimulating effect of adaptogens: an overview with particular reference to their efficacy following single dose administration

Panossian

Wagner²

2005

Phytother. Res.

163

117

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Plant adaptogens are compounds that increase the ability of an organism to adapt to environmental factors and to avoid damage from such factors. The beneficial effects of multidose administration of adaptogens are mainly associated with the hypothalamic-pituitaryadrenal (HPA) axis, a part of the stress-system that is believed to play a primary role in the reactions of the body to repeated stress and adaptation. In contrast, the single dose application of adaptogens is important in situations that require a rapid response to tension or to a stressful situation. In this case, the effects of the adaptogens are associated with another part of the stress-system, namely, the sympatho-adrenal-system (SAS), that provides a rapid response mechanism mainly to control the acute reaction of the organism to a stressor. This review focuses primarily on the SAS-mediated stimulating effects of single doses of adaptogens derived from Rhodiola rosea, Schizandra chinensis and Eleutherococcus senticosus. The use of these drugs typically generates no side effects, unlike traditional stimulants that possess addiction, tolerance and abuse potential, produce a negative effect on sleep structure, and cause rebound hypersomnolence or "come down" effects. Furthermore, single administration of these adaptogens effectively increases mental performance and physical working capacity in humans. R. rosea is the most active of the three plant adaptogens producing, within 30 min of administration, a stimulating effect that continues for at least 4 -6 h. The active principles of the three plants that exhibit single dose stimulating effects are glycosides of phenylpropane-and phenylethane-based phenolic compounds such as salidroside, rosavin, syringin and triandrin, the latter being the most active.

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Section: Effect Of Adaptogens On Physical Working Capacitymentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Stimulating effect of adaptogens: an overview with particular reference to their efficacy following single dose administration

Panossian

Wagner²

2005

Phytother. Res.

163

117

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“…They carried out numerical experiments with orderings of parameters of Young and of Lebedev-Finogenov [5]. They concluded that for illconditioned systems (i.e.…”

Section: Introductionmentioning

confidence: 98%

“…For example, the natural ordering of the parameters Pl, P2 ..... Pu see (2.3) and (2.4), leads to overflow after a few steps. Some orderings of the parameters that were proposed in the literature, see [5] for a review, reduce the instability partially. The problem of finding an ordering which makes the nonstationary Richardson iteration computationally stable was first solved by Lebedev and Finogenov in [5].…”

Section: Introductionmentioning

confidence: 98%

“…Some orderings of the parameters that were proposed in the literature, see [5] for a review, reduce the instability partially. The problem of finding an ordering which makes the nonstationary Richardson iteration computationally stable was first solved by Lebedev and Finogenov in [5]. Later using a different approach the same ordering was constructed in [7].…”

Section: Introductionmentioning

confidence: 98%

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Numerical stability of the cyclic Richardson iteration

Zawilski¹

1991

Numer. Math.

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Summary. The succc~s of the cyclic Richardson iteration depends on the properordering of the acceleration parameters. We give a rigorous error analysis to show that, with the proper ordering, the relative error in the iterative method, when properly terminated, is not larger than the error incurred in stable direct methods such as Cholesky factorization. For both the computed approximation fi to u = L-if satisfies Ilu-~ll < cond(L)lluH2 -t and this bound is attainable. We also show that the residual norm IIf -L~II is bounded by HLllcond(L) 11~l12-t. This bound is attainable for a small cycle length N. Our analysis suggests that for a larger cycle length N the residuals are bounded by liE II [I~H2-t. We construct a theoretical example in which this bound is attainable. However we observed in all numerical tests that ultimately the residual norms were of order [ILII 11~112 -t. We explain why in practice even the factor ~ is never encountered. Therefore the residual stopping criterion for the Richardson iteration appears to be very reliable and the method itself appears to be stable.

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