Titlebook: Approximation Theory XV: San Antonio 2016; Gregory E. Fasshauer,Larry L. Schumaker Conference proceedings 2017 Springer International Publ

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https://doi.org/10.1007/978-3-663-20379-7ultimate goal is to find a PDE-solution-dependent triangulation which improves both the accuracy and computational efficiency of the spline solution. We present little theory to guide our search for such a triangulation, but instead approach the problem numerically. Starting with some initial triang

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https://doi.org/10.1007/978-3-663-20379-7 Fourier transform . of a nonzero compactly supported scalar-valued function satisfying the refinement equation . with . dilation . does not vanish at infinity so by the Riemann–Lebesgue lemma . is not integrable. Dai, Feng, and Wang [.] extended his result to scalar-valued solutions of . where . ar

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Günter Blunk,Klaus Kraß,Jan Kollarplines on triangulations with hanging vertices. Allowing triangulations with hanging vertices provides much more flexibility than using ordinary triangulations and allows for simple adaptive algorithms based on local refinements. The use of these techniques is illustrated for two application areas o

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Günter Blunk,Klaus Kraß,Jan Kollarhand side, we have ., where . is a polynomial of degree ., and on the right, an entire function of exponential type. We discuss the role of this type of scaling limit in a number of topics: Bernstein’s constant for approximation of .; universality limits for random matrices; asymptotics of . Christo

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https://doi.org/10.1007/978-3-663-07203-4of Tchebycheffian B-splines and form an attractive alternative to standard polynomial B-splines and NURBS in both modeling and simulation. We summarize their definition and main properties, and we illustrate their use in a selection of numerical examples in the context of isogeometric analysis. For

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,Kurzfassung des Abschlußberichtes,e show that by distributing the batches computationally, a significant speedup in the convergence rate is provably possible compared to either batched sampling or weighted sampling alone. We propose several computationally efficient schemes to approximate the optimal weights and compute proposed sam

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,Kurzfassung des Abschlußberichtes,e., the fractional-order logistic equation. The use of the fractional B-splines allows us to express the fractional derivatives of the approximating function in an analytical form. Thus, the fractional collocation method is easy to implement, accurate, and efficient. Several numerical tests illustra

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