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128
Dual Pricing of MultiExercise Options under Volume Constraints
, 2009
"... The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distrib ..."
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Cited by 137 (8 self)
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The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distributed by the authors. Dual pricing of multiexercise options under volume constraints
Minimization of Nonsmooth, Nonconvex Functionals by Iterative Thresholding
, 2009
"... Preprint 10The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will ..."
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Cited by 128 (2 self)
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Preprint 10The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distributed by the authors. Minimization of nonsmooth, nonconvex functionals by iterative thresholding
CurveletWavelet Regularized Split Bregman Iteration for Compressed Sensing
"... Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows to recover this signal from much fewer samples than the ShannonNyquist theory requires. Many images ..."
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Cited by 119 (6 self)
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Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows to recover this signal from much fewer samples than the ShannonNyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent pointlike features while curvelets represent linelike features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + ɛ with the measurement matrix Φ ∈ R K×N, K<<N, we consider a jointly sparsityconstrained optimization problem of the form argmin{‖ΛcΨcu‖1 + ‖ΛwΨwu‖1 + u 1 2‖f − Φu‖22}. Here Ψcand Ψw are the transform matrices corresponding to the two frames, and the diagonal matrices Λc, Λw contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the DouglasRachford Split algorithm. Numerical experiments for compressed sensing based Fourierdomain random imaging show good performances of the proposed curveletwavelet regularized split Bregman (CWSpB) methods,whereweparticularlyuseacombination of wavelet and curvelet coefficients as sparsity constraints.
Error bounds for computing the expectation by Markov chain Monte Carlo
, 2009
"... We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to the l2, l4 and l∞norm of the function are proven. By the estimation the well known asymptotical limit of the error is attained, i.e. there is n ..."
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Cited by 117 (2 self)
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We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to the l2, l4 and l∞norm of the function are proven. By the estimation the well known asymptotical limit of the error is attained, i.e. there is no gap between the estimate and the asymptotical behavior. We discuss the dependence of the error on a burnin of the Markov chain. Furthermore we suggest and justify a specific burnin for optimizing the algorithm.
Optimally Sparse Image Representation by the Easy Path Wavelet Transform
, 2009
"... Abstract The Easy Path Wavelet Transform (EPWT) ..."
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Nonequispaced hyperbolic cross fast Fourier transform
"... A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like the fast Fourier transform (FFT) have high computational costs. Hyperbolic cross approximations allow for a severe decre ..."
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Cited by 113 (3 self)
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A straightforward discretisation of problems in d spatial dimensions often leads to an exponential growth in the number of degrees of freedom. Thus, even efficient algorithms like the fast Fourier transform (FFT) have high computational costs. Hyperbolic cross approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives. We propose a nonequispaced hyperbolic cross fast Fourier transform based on one hyperbolic cross FFT and a dedicated interpolation by splines on sparse grids. Analogously to the nonequispaced FFT for trigonometric polynomials with Fourier coefficients supported on the full grid, this allows for the efficient evaluation of trigonometric polynomials with Fourier coefficients supported on the hyperbolic cross at arbitrary spatial sampling nodes. Key words and phrases: trigonometric approximation, hyperbolic cross, sparse grid, fast Fourier transform, nonequispaced FFT
Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise
, 2009
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A New Hybrid Method for Image Approximation using the Easy Path Wavelet Transform
"... The Easy Path Wavelet Transform (EPWT) has recently been proposed by one of the authors as a tool for sparse representations of bivariate functions from discrete data, in particular from image data. The EPWT is a locally adaptive wavelet transform. It works along pathways through the array of functi ..."
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Cited by 111 (4 self)
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The Easy Path Wavelet Transform (EPWT) has recently been proposed by one of the authors as a tool for sparse representations of bivariate functions from discrete data, in particular from image data. The EPWT is a locally adaptive wavelet transform. It works along pathways through the array of function values and exploits the local correlations of the given data in a simple appropriate manner. However, the EPWT suffers from its adaptivity costs that arise from the storage of path vectors. In this paper, we propose a new hybrid method for image compression that exploits the advantages of the usual tensor product wavelet transform for the representation of smooth images and uses the EPWT for an efficient representation of edges and texture. Numerical results show the efficiency of this procedure. Key words. sparse data representation, tensor product wavelet transform, easy path wavelet transform, linear diffusion, smoothing filters, adaptive wavelet bases, Nterm approximation AMS Subject classifications. 41A25, 42C40, 68U10, 94A08 1
An Error Analysis of The Multiconfiguration Timedependent Hartree Method of Quantum Dynamics
 MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
, 2010
"... This paper gives an error analysis of the multiconfiguration timedependent Hartree (MCTDH) method for the approximation of multiparticle timedependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions a ..."
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Cited by 111 (0 self)
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This paper gives an error analysis of the multiconfiguration timedependent Hartree (MCTDH) method for the approximation of multiparticle timedependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the highdimensional linear Schrödinger equation by a coupled system of ordinary differential equations and lowdimensional nonlinear partial differential equations. The main result of this paper yields an L 2 error bound of the MCTDH approximation in terms of a bestapproximation error bound in a stronger norm and of lower bounds of singular values of matrix unfoldings of the coefficient tensor. This result permits us to establish convergence of the MCTDH method to the exact wave function under appropriate conditions on the approximability of the wave function, and it points to reasons for possible failure in other cases.