Austrian Academy of Sciences

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften
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    Ulbrich, Franz

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    * 10.4.1762 Müglitz/Mähren (Mohelnice/CZ), † 27.11.1826 Leopoldstadt (Wien II). Musiker

    Pseudo-linear convergence of an additive Schwarz method for dual total variation minimization. ETNA - Electronic Transactions on Numerical Analysis

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    In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation. The O(1/n)-energy convergence of the proposed method is proven, where n is the number of iterations. In addition, we introduce an interesting convergence property of the proposed method called pseudo-linear convergence; the energy decreases as fast as for linearly convergent algorithms until it reaches a particular value. It is shown that this particular value depends on the overlapping width δ, and the proposed method becomes as efficient as linearly convergent algorithms if δ is large. As the latest domain decomposition methods for total variation minimization are sublinearly convergent, the proposed method outperforms them in the sense of the energy decay. Numerical experiments which support our theoretical results are provided

    New fractional pseudospectral methods with accurate convergence rates for fractional differential equations. ETNA - Electronic Transactions on Numerical Analysis

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    The main purpose of this paper is to introduce generalized fractional pseudospectral integration and differentiation matrices using a family of fractional interpolants, called fractional Lagrange interpolants. We develop novel approaches to the numerical solution of fractional differential equations with a singular behavior at an end-point. To achieve this goal, we present efficient and stable methods based on three-term recurrence relations, generalized barycentric representations, and Jacobi-Gauss quadrature rules to evaluate the corresponding matrices. In a special case, we prove the equivalence of the proposed fractional pseudospectral methods using a suitable fractional Birkhoff interpolation problem. In fact, the fractional integration matrix yields the stable inverse of the fractional differentiation matrix, and the resulting system is well-conditioned. We develop efficient implementation procedures for providing optimal error estimates with accurate convergence rates for the interpolation operators and the proposed schemes in the L2L^{2}-norm. Some numerical results are given to illustrate the accuracy and performance of the algorithms and the convergence rates

    Early Bronze Age metal workshops at Çukuriçi Höyük Production of arsenical copper at the beginning of the 3rd millennium BC

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    Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften is based in Austria
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