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Ortiz-Gracia, L. (author), Oosterlee, C.W. (author)We present a novel method for pricing European options based on the wavelet approximation method and the characteristic function. We focus on the discounted expected payoff pricing formula and compute it by means of wavelets. We approximate the density function associated to the underlying asset price process by a finite combination of jth order...journal article 2013
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Jansen, J.D. (author)Controlling the flow of fluids (e.g. water, oil, natural gas or CO2) in subsurface porous media is a technical process with many mathematical challenges. The underlying physics can be described with coupled nearly-elliptic and nearly-hyperbolic nonlinear partial differential equations, which require the aid of large-scale numerical simulation....lecture notes 2013
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Labeur, R.J. (author), Wells, G.N. (author)A hybrid method for the incompressible Navier–Stokes equations is presented. The ethod inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods hen momentum advection becomes significant, equal-order interpolations can be used for the velocity nd pressure fields, and mass can be conserved locally. Using continuous...journal article 2012
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Mirzaee, H. (author), Li, L. (author), Ryan, J.K. (author), Kirby, R.M. (author)Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order $k$+1 to 2$k$+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform...journal article 2011
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Mailybaev, A.A. (author), Marchesin, D. (author), Bruining, J. (author)This paper analyzes traveling wave profiles possessing an internal resonance point for a class of systems of partial differential equations describing oxidation and vaporization of liquid fuel in a porous medium when an oxidizer (air) is injected. It is shown that the resonance is characterized by a saddle point of an associated vector field...journal article 2011
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Van Slingerland, P. (author), Ryan, J.K. (author), Vuik, C. (author)Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering is a promising technique not only in improving the order of the numerical solution obtained by a discontinuous Galerkin (DG) method but also in increasing the smoothness of the field and improving the magnitude of the errors. This was initially established as an...journal article 2011
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Lampe, J. (author), Rojas, M. (author), Sorensen, D.C. (author), Voss, H. (author)The LSTRS software for the efficient solution of the large-scale trust-region subproblem was proposed in [M. Rojas, S. A. Santos, and D. C. Sorensen, ACM Trans. Math. Software, 34 (2008), article 11]. The LSTRS method is based on recasting the problem in terms of a parameter-dependent eigenvalue problem and adjusting the parameter iteratively....journal article 2011
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Campbell, A. (author), Nazarov, S.A. (author), Sweers, G.H. (author)We investigate the spectrum of the two-dimensional model for a thin plate with a sharp edge. The model yields an elliptic $3\times3$ Agmon–Douglis–Nirenberg system on a planar domain with coefficients degenerating at the boundary. We prove that in the case of a degeneration rate $\alpha<2$, the spectrum is discrete, but, for $\alpha\geq2$, there...journal article 2010
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Alpern, S. (author), Fokkink, R.J. (author), Kikuta, K. (author)In an accumulation game, the Hider secretly distributes his given total wealth $h$ among $n$ locations, while the Searcher picks $r$ locations and confiscates the material placed there. The Hider wins if what is left at the remaining $n-r$ locations is at least 1; otherwise the Searcher wins. Ruckle's conjecture says that an optimal Hider...journal article 2010
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Lesaja, G. (author), Roos, C. (author)We present an interior-point method for the P?(?)-linear complementarity problem (LCP) that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. This class is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non...journal article 2010
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Rodrigo, C. (author), Gaspar, F.J. (author), Oosterlee, C.W. (author), Yavneh, I. (author)The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted ElFMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for...journal article 2010
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Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author)IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...journal article 2010
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Frijlink, M. (author), Wapenaar, C.P.A. (author)One-way wave equations conveniently describe wave propagation in media with discontinuous and/or rapid variations in one direction, but with smooth and slow variations in the complementary transverse directions. In the past, reciprocity theorems have been developed in terms of one-way wave fields. The boundaries of the integration volumes and...journal article 2010
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Chandrasekaran, S. (author), Dewilde, P. (author), Gu, M. (author), Somasunderam, N. (author)It is shown that the numerical rank of the off-diagonal blocks of certain Schur complements of matrices that arise from the finite-difference discretization of constant coefficient, elliptic PDEs in two spatial dimensions is bounded by a constant independent of the grid size. Moreover, in three-dimensional problems the Schur complements are...journal article 2010
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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an...journal article 2010
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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems via shape-linearization principles. To derive an appropriate dual (linearized adjoint) problem, we linearize the domain dependence of the very weak form and goal functional of interest using techniques from shape calculus. We show...journal article 2010
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Byrka, J. (author), Aardal, K.I. (author)We obtain a 1.5-approximation algorithm for the metric uncapacitated facility location (UFL) problem, which improves on the previously best known 1.52-approximation algorithm by Mahdian, Ye, and Zhang. Note that the approximability lower bound by Guha and Khuller is 1.463 . . . . An algorithm is a (?f ,?c)-approximation algorithm if the solution...journal article 2010
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Tang, J.M. (author), MacLachlan, S.P. (author), Nabben, R. (author), Vuik, C. (author)It is well known that two-level and multilevel preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a...journal article 2010
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Gu, G. (author), Roos, C. (author)In [SIAM J. Optim., 16 (2006), pp. 1110–1136], Roos proved that the devised full-step infeasible algorithm has $O(n)$ worst-case iteration complexity. This complexity bound depends linearly on a parameter $\bar{\kappa}(\zeta)$, which is proved to be less than $\sqrt{2n}$. Based on extensive computational evidence (hundreds of thousands of...journal article 2010
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- Mikeli?, A. (author), Bruining, J. (author) journal article 2008
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