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1.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
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Compounds of the series PhnMe6–nSn2 were prepared and tested for their antifeedant effects against Spodoptera littoralis (Boisduval) and Epilachna varivestis (Mulsant) larvae. In addition, phytotoxicity towards bean seedlings was measured. The most active compound against both Spodoptera and Epilachna was Ph3Me3Sn2. The compound at 50 mg dm?3 was comparatively innocuous in phytotoxicity tests against bean seedlings. 相似文献
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Ascher P Audirac L Adimi N Blank B Borcea C Brown BA Companis I Delalee F Demonchy CE de Oliveira Santos F Giovinazzo J Grévy S Grigorenko LV Kurtukian-Nieto T Leblanc S Pedroza JL Perrot L Pibernat J Serani L Srivastava PC Thomas JC 《Physical review letters》2011,107(10):102502
The two protons emitted in the decay of 54Zn have been individually observed for the first time in a time projection chamber. The total decay energy and the half-life measured in this work agree with the results obtained in a previous experiment. Angular and energy correlations between the two protons are determined and compared to theoretical distributions of a three-body model. Within the shell model framework, the relative decay probabilities show a strong contribution of the p2 configuration for the two-proton emission. After 45Fe, the present result on 54Zn constitutes only the second case of a direct observation of the ground state two-proton decay of a long-lived isotope. 相似文献
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Lorien J. Parker Louis C. Italiano Craig J. Morton Nancy C. Hancock David B. Ascher Jade B. Aitken Hugh H. Harris Pablo Campomanes Ursula Rothlisberger Anastasia De Luca Mario Lo Bello Wee Han Ang Paul J. Dyson Michael W. Parker 《Chemistry (Weinheim an der Bergstrasse, Germany)》2011,17(28):7705-7705
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Taking into account the fact that space groups are groups of transformations of Euclideann-dimensional space, non-equivalent systems of non-primitive translations are defined. They can be brought into one-to-one correspondence with the elements of the groupH 1 (K, R n /Z n ) or with those of the groupH 1 (K, Z n /kZ n )/H 1 (K, Z n ). (K is a point group of orderk.) The consistency of these findings with the results of Part I is given by the isomorphisms $$H^2 (K,Z^n ) \cong H^1 (K,R^n /Z^n ) \cong H^1 (K,Z^n /kZ^n )/H^1 (K,Z^n ).$$ Theorems are proved giving the conditions for cohomology groupsH q (K, A) to be zero. These conditions are fulfilled in particular ifA=R n andK is a subgroup ofGL (n, R) that either is compact (thenq>0) or has a finite normal subgroup leaving no element ofR n invariant (thenq≧0). This implies that the affine, the Euclidean and the inhomogeneous Lorentz groups are the only extensions ofR n by the corresponding homogeneous groups. By way of illustration, the theory of this paper is applied to two 2-dimensional space groups. 相似文献