Thèse de doctorat : Università della Svizzera italiana, 2009 ; 2009INFO003.
Approximation algorithms are motivated by the fact that for many important optimization problems we cannot hope to efficiently find an optimal solution (unless P=NP). Instead, we have to settle for second best — a solution that is close to being optimal. A natural question that arises is: how close to the optimal solution can one get with an efficient algorithm? The past two decades have...
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In: Applied and Computational Harmonic Analysis, 2007, vol. 23, no. 3, p. 307-320
We consider the Hermite trigonometric interpolation problem of order 1 for equidistant nodes, i.e., the problem of finding a trigonometric polynomial t that interpolates the values of a function and of its derivative at equidistant points. We give a formula for the Fourier coefficients of t in terms of those of the two classical trigonometric polynomials interpolating the values and those of the...
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In: Numerical Algorithms, 2007, vol. 45, no. 1-4, p. 369-374
Sinc-interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. It, however, requires that the interpolated function decreases rapidly or is periodic. We give an error formula for the case where neither of these conditions is satisfied.
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In: Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2004, vol. 66, no. 4, p. 893–908
Generalized Linear Latent Variable Models (GLLVM), as defined in Bartholomew and Knott (1999) enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must...
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In: Journal of Econometrics, 2001, vol. 101, no. 1, p. 37-69
The local robustness properties of Generalized Method of Moments (GMM) estimators and of a broad class of GMM based tests are investigated in a unified framework. GMM statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded. Since in many applications this function is unbounded, it is useful to...
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In: Chemical Communications, 2006, p. 4495-4497
Oxidative addition of pyridyl-functionalised 4-iodoimidazolium salts to palladium(0) gives catalytically active complexes in which the N-heterocyclic carbene is bound to the palladium(II) centre in a non-classical bonding mode via C(4).
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In: Journal of Computational and Applied Mathematics, 2006, vol. 189(1-2), p. 375-386
The present work makes the case for viewing the Euler–Maclaurin formula as an expression for the effect of a jump on the accuracy of Riemann sums on circles and draws some consequences thereof, e.g., when the integrand has several jumps. On the way we give a construction of the Bernoulli polynomials tailored to the proof of the formula and we show how extra jumps may lead to a smaller...
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In: Journal of Computational and Applied Mathematics, 2004, vol. 164-165, p. 81
Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the...
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Thèse de doctorat : Université de Fribourg, 2000 ; No 1313.
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In: Journal of Computational Physics, 2005, vol. 204, p. 292-301
Due to their rapid – often exponential – convergence as the number N of interpolation/collocation points is increased, polynomial pseudospectral methods are very efficient in solving smooth boundary value problems. However, when the solution displays boundary layers and/or interior fronts, this fast convergence will merely occur with very large N. To address this difficulty, we present a...
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