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Palabra: OPTIMAL COMPUTATIONAL COMPLEXITY (Palabras)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Stevenson, Rob
Título: Adaptive Solution of Operator Equations Using Wavelet Frames
Páginas/Colación: pp. 1074 - 1100
Url: Ir a http://epubs.siam.org/sam-bin/dbq/article/40798http://epubs.siam.org/sam-bin/dbq/article/40798
Siam Journal on Numerical Analysis Vol. 41, no. 3 May/July 2004
Información de existenciaInformación de existencia

Palabras Claves: Palabras: ADAPTIVE METHODS ADAPTIVE METHODS, Palabras: BEST \(N\)-TERM APPROXIMATION BEST \(N\)-TERM APPROXIMATION, Palabras: FRAMES FRAMES, Palabras: OPERATOR EQUATIONS OPERATOR EQUATIONS, Palabras: OPTIMAL COMPUTATIONAL COMPLEXITY OPTIMAL COMPUTATIONAL COMPLEXITY, Palabras: WAVELETS WAVELETS

Resumen
In "Adaptive wavelet methods II---Beyond the elliptic case" of Cohen, Dahmen, and DeVore [Found. Comput. Math., 2 (2002), pp. 203--245], an adaptive method has been developed for solving general operator equations. Using a Riesz basis of wavelet type for the energy space, the operator equation is transformed into an equivalent matrix-vector system. This system is solved iteratively, where the application of the infinite stiffness matrix is replaced by an adaptive approximation. Assuming that the stiffness matrix is sufficiently compressible, i.e., that it can be sufficiently well approximated by sparse matrices, it was proved that the adaptive method has optimal computational complexity in the sense that it converges with the same rate as the best N-term approximation for the solution, assuming that the latter would be explicitly available. The condition concerning compressibility requires that, dependent on their order, the wavelets have sufficiently many vanishing moments, and that they be sufficiently smooth. However, except on tensor product domains, wavelets that satisfy this smoothness requirement are not easy to construct. In this paper we write the domain or manifold on which the operator equation is posed as an overlapping union of subdomains, each of them being the image under a smooth parametrization of the hypercube. By lifting wavelets on the hypercube to the subdomains, we obtain a {\em frame} for the energy space. With this frame the operator equation is transformed into a matrix-vector system, after which this system is solved iteratively by an adaptive method similar to the one from the work of Cohen, Dahmen, and DeVore. With this approach, frame elements that have sufficiently many vanishing moments and are sufficiently smooth, something needed for the compressibility, are easily constructed. By handling additional difficulties due to the fact that a frame gives rise to an underdetermined matrix-vector system, we prove that this adaptive method has optimal computational complexity.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Fumagalli, Andrea ; Valcarenghi, Luca
Título: IP restoration vs. WDM protection: Is there an optimal choice
Páginas/Colación: pp. 34-41
IEEE Network Vol. 14, no. 6 Nov/Dec 2000
Información de existenciaInformación de existencia

Resumen
The exponentially growing number of Internet users armed with emerging multimedia Internet applications is continuously thirsty for more network capacity

The exponentially growing number of Internet users armed with emerging multimedia Internet applications is continuously thirsty for more network capacity. Wavelength-division multiplexing networks that directly support IP-the so-called IP over WDM architecture-have the appropriate characteristics to quench this bandwidth thirst. As everyday life increasingly relies on telecommunication services, users become more and more demanding, and connection reliability is currently as critical as high capacity. Both IP and WDM layers can fulfill this need by providing various resilient schemes to protect users' traffic from disruptions due to network faults. This article first reviews the most common restoration and protection schemes available at the IP and WDM layers. These schemes may be present concurrently in the IP over WDM architecture, with the resilient mechanism of each connection specifically chosen as a function of the overall cost, application requirements, and management complexity. The second part of the article describes a versatile heuristic based on simulated annealing that may be adopted to optimize the concurrent use of IP restoration and WDM protection schemes in the same (mesh) network. The proposed heuristic allows varying the percentage of traffic protected by the WDM layer and that of traffic relying on IP restoration, taking into account topology constraints and network cost minimization. An additional feature of the proposed heuristic is the potential to trade solution optimality for computational time, thus yielding fast solutions in support of interactive design.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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