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Vuik, M.J. (author), Ryan, J.K. (author)In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138160] we studied the use of troubledcell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problemdependent...journal article 2016
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Ruijter, M.J. (author), Oosterlee, C.W. (author)We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general thetadiscretization of the timeintegrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier cosine series expansions, relying on the availability of a characteristic function. The method is...journal article 2015
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Roos, C. (author)We present an improved version of an infeasible interiorpoint method for linear optimization published in 2006. In the earlier version each iteration consisted of one socalled feasibility step and a fewat most threecentering steps. In this paper each iteration consists of only a feasibility step, whereas the iteration bound improves the...journal article 2015
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Alpern, S. (author), Fokkink, R. (author), Gal, S. (author), Timmer, M. (author)We present a stochastic game that models ambush/search in a finite region Q which has area but no other structure. The searcher can search a unit area of Q in unit time or adopt an "ambush" mode for a certain period. The searcher "captures" the hider when the searched region contains the hider's location or if the hider moves while the searcher...journal article 2013
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Esmaeil Zadeh Soudjani, S. (author), Abate, A. (author)This work is concerned with the generation of finite abstractions of general statespace processes to be employed in the formal verification of probabilistic properties by means of automatic techniques such as probabilistic model checkers. The work employs an abstraction procedure based on the partitioning of the statespace, which generates a...journal article 2013
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Zhang, B. (author), Oosterlee, C.W. (author)We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European style and Americanstyle Asian options and for discretely and continuously monitored versions. In the present paper...journal article 2013
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Druskin, V. (author), Remis, R.F. (author)The Krylov subspace projection approach is a wellestablished tool for the reducedorder modeling of dynamical systems in the time domain. In this paper, we address the main issues obstructing the application of this powerful approach to the timedomain solution of exterior wave problems. We use frequencyindependent perfectly matched layers to...journal article 2013
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Wapenaar, C.P.A. (author), Thorbecke, J.W. (author)The crosscorrelation of ambient acoustic noise observed at two receivers yields the impulse response between these receivers, assuming that the noise field is diffuse. In practical situations the noise field exhibits directionality, which imprints the angledependent correlation function. For the situation of a directional scatterer in a...journal article 2013
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), Vuik, C. (author), Scarpas, A. (author)Large discontinuities in material properties, such as those encountered in composite materials, lead to illconditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper...journal article 2013
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Mirzaee, H. (author), King, J. (author), Ryan, J.K. (author), Kirby, R.M. (author)The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with...journal article 2013
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Ruijter, M.J. (author), Oosterlee, C.W. (author)The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 2762]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price...journal article 2012
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Sonneveld, P. (author)An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials...journal article 2012
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 Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author) journal article 2012
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Zouros, G.P. (author), Budko, N.V. (author)The domain integral equation method with its FFTbased matrixvector products is a viable alternative to local methods in freespace scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify very dense...journal article 2012
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Maggiore, B. (author), Rawn, B.G. (author), Lehn, P. (author)The problem of determining invariance kernels for planar singleinput nonlinear systems is considered. If K is a closed set, its invariance kernel is the largest subset of K with the property of being positively invariant for arbitrary measurable input signals. It is shown that the boundary of the invariance kernel is a concatenation of...journal article 2012
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Huang, X. (author), Oosterlee, C.W. (author)We derive two types of saddlepoint approximations for expectations in the form of E[(X  K)+], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the independently and identically distributed case. The approximations are further extended to...journal article 2011
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Fang, F. (author), Oosterlee, C.W. (author)We develop an efficient Fourierbased numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The twodimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C.W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826–848...journal article 2011
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