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An adaptive pruning algorithm for the discrete L-curve criterion 总被引:1,自引:0,他引:1
Per Christian Hansen Toke Koldborg Jensen Giuseppe Rodriguez 《Journal of Computational and Applied Mathematics》2007
We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples. 相似文献
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Johann Guilleminot Christian Soize Djimedo Kondo Christophe Binetruy 《International Journal of Solids and Structures》2008,45(21):5567-5583
Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen–Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. In particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered. 相似文献
27.
Christian Hainzl Vitali Vougalter Semjon A. Vugalter 《Communications in Mathematical Physics》2003,233(1):13-26
We consider a spinless particle coupled to a photon field and prove that even if the Schr?dinger operator p
2
+V does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian
and our result holds in the case where the coupling constant α is small.
Received: 7 January 2002 / Accepted: 8 November 2002 Published online: 13 January 2003 相似文献
28.
Vladimir B. Arion Alexey A. Nazarov Christian G. Hartinger Gerald Giester Bernhard K. Keppler 《应用有机金属化学》2003,17(9):723-724
For the unsymmetrical title compound, 1‐bromo‐1′‐[(2S)‐N‐(1‐hydroxy‐3‐methylbutane‐2‐yl)]‐ferroceneamide, two independent molecules were found in the asymmetric unit. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
29.
Christian Kluger Wolfgang H. Binder 《Journal of polymer science. Part A, Polymer chemistry》2007,45(3):485-499
Block copolymers on basis of poly(oxanorbornenes) bearing functional moieties in their side‐chains are prepared via a combination of ROMP‐methods and 1,3‐dipolar‐“click”‐reactions. Starting from N‐substituted‐ω‐bromoalkyl‐oxanorbornenes and alkyl‐/perfluoroalkyl‐oxanorbornenes, block copolymers with molecular weights up to 25,000 g mol?1 were generated. Subsequent nucleophilic exchange‐reactions yielded the block‐copolymers functionalized with ω‐azidoalkyl‐moieties in one block. The 1,3‐azide/alkine‐“click” reactions with a variety of terminal alkynes in the presence of a catalyst system consisting of tetrakis(acetonitrile)hexafluorophosphate copper(I) and tris(1‐benzyl‐5‐methyl‐1H‐ [1,2,3]triazol‐4‐ylmethyl)‐amine furnished the substituted block copolymers in high yields, as proven by NMR‐spectroscopy. The resulting polymers were investigated via temperature‐dependent SAXS‐methods, revealing their microphase separated structure as well as their temperature‐dependent behavior. The presented method offers the generation of a large set of different block‐copolymers from only a small set of starting materials because of the high versatility of the “click” reaction, thus enabling a simple and complete functionalization after the initial polymerization reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 485–499, 2007 相似文献
30.
Christian Buchgraber Alexander Pogantsch Stefan Kappaun Julia Spanring Wolfgang Kern 《Journal of polymer science. Part A, Polymer chemistry》2006,44(14):4317-4327
Light‐emitting diodes based on organic materials [organic light‐emitting diodes (OLEDs)] have attracted much interest over the past decade. Several different attempts have been made to realize multicolor OLEDs. This article describes a new approach based on energy transfer in a donor/acceptor system. A copolymer containing both donor and acceptor compounds as comonomer units is prepared. The polymer consists of a derivative of a luminescent dye [4‐dicyanmethylene‐2‐methyl‐6‐4H‐pyran (DCM); acceptor compound], which is copolymerized with fluorene (donor compound) to combine the properties of an electroactive polymer with a highly luminescent dye. Photochemical processing is achieved by UV irradiation of this copolymer in the presence of gaseous trialkylsilanes. This reagent selectively saturates the C?C bonds in the DCM comonomer units while leaving the fluorene units essentially unaffected. As a result of the photochemical process, the red electroluminescence of the acceptor compound vanishes, and the blue‐green electroluminescence from the polyfluorene units is recovered. Compared with previous approaches based on polymer blends, this copolymer approach avoids problems associated with phase‐separation phenomena in the active layer of OLEDs. © 2006Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4317–4327, 2006 相似文献