#### DMCA

## On the stability of the hyperbolic cross discrete Fourier transform

### Cached

### Download Links

Citations: | 103 - 2 self |

### Citations

214 |
Sparse Grids.
- Bungartz, Griebel
- 2004
(Show Context)
Citation Context ...bolic crosses has led to problems of total size Cd2nnd−1. Moreover, the approximation rate hardly deteriorates for functions in an appropriate scale of spaces of dominating mixed smoothness, see e.g. =-=[12, 14, 9, 8, 11, 2, 10, 13]-=-. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also [5] for a recent generali... |

177 | Hierarchical singular value decomposition of tensors - Grasedyck |

143 | Multilevel Monte Carlo Algorithms for Lévy-driven SDEs with Gaussian Correction - Dereich - 2009 |

137 | The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-dimensional Data
- Plonka
- 2008
(Show Context)
Citation Context ...bolic crosses has led to problems of total size Cd2nnd−1. Moreover, the approximation rate hardly deteriorates for functions in an appropriate scale of spaces of dominating mixed smoothness, see e.g. =-=[12, 14, 9, 8, 11, 2, 10, 13]-=-. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also [5] for a recent generali... |

137 | Dual Pricing of Multi-Exercise Options under Volume Constraints
- Bender
- 2009
(Show Context)
Citation Context ...bolic crosses has led to problems of total size Cd2nnd−1. Moreover, the approximation rate hardly deteriorates for functions in an appropriate scale of spaces of dominating mixed smoothness, see e.g. =-=[12, 14, 9, 8, 11, 2, 10, 13]-=-. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also [5] for a recent generali... |

134 | Optimal Approximation of Elliptic Problems by Linear and Nonlinear - Dahlke, Novak, et al. - 2009 |

134 | Computing Semi-classical Quantum Dynamics with Hagedorn Wavepackets - Faou, Gradinaru, et al. - 2009 |

133 | Approximation of Infinitely Differentiable Multivariate
- Novak, Woźniakowski
- 2009
(Show Context)
Citation Context ...hness, see e.g. [12, 14, 9, 8, 11, 2, 10, 13]. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in =-=[1, 7, 6]-=-, see also [5] for a recent generalisation to arbitrary spatial sampling nodes and [4] for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross dis... |

131 | Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion
- Denis, Lorenz, et al.
- 2009
(Show Context)
Citation Context |

129 |
Black Box Low Tensor Rank Approximation Using Fibre-Crosses
- Espig, Grasedyck, et al.
- 2008
(Show Context)
Citation Context ...isation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also [5] for a recent generalisation to arbitrary spatial sampling nodes and =-=[4]-=- for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross discrete Fourier transform, which of course limits the stability of a particular and pote... |

128 | A Review of Curvelets and Recent Applications
- Ma, Plonka
- 2009
(Show Context)
Citation Context ...hness, see e.g. [12, 14, 9, 8, 11, 2, 10, 13]. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in =-=[1, 7, 6]-=-, see also [5] for a recent generalisation to arbitrary spatial sampling nodes and [4] for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross dis... |

128 | Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding
- Bredies, Lorenz
- 2009
(Show Context)
Citation Context |

128 | Regularization with Non-convex Separable Constraints
- Bredies, Lorenz
- 2009
(Show Context)
Citation Context |

124 | A Compressive Landweber Iteration for Solving Ill-Posed Inverse Problems
- Ramlau, Teschke, et al.
- 2008
(Show Context)
Citation Context ...hness, see e.g. [12, 14, 9, 8, 11, 2, 10, 13]. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in =-=[1, 7, 6]-=-, see also [5] for a recent generalisation to arbitrary spatial sampling nodes and [4] for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross dis... |

122 | Adaptive Wavelet Methods and Sparsity Reconstruction for Inverse Heat Conduction Problems
- Bonesky, Dahlke, et al.
- 2009
(Show Context)
Citation Context ... 14, 9, 8, 11, 2, 10, 13]. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also =-=[5]-=- for a recent generalisation to arbitrary spatial sampling nodes and [4] for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross discrete Fourier ... |

120 | Optimal Order of Convergence and (In-) Tractability of Multivariate Approximation of Smooth Functions
- Novak, Woźniakowski
- 2008
(Show Context)
Citation Context ...2piikx)k∈Ĝj ,x∈Gj , where F j := (e2piikx)x∈Gj ,k∈Ĝj = F j1 ⊗ . . .⊗ F jd denotes the ordinary Fourier matrix. Next, we turn to the trigonometric interpolation on the sparse grid, see the monograph =-=[3]-=- for an introduction. In what follows, the interpolation operator allows for a Boolean sum decomposition which is used for analysing the associated Fourier matrix. For d ∈ N, n ∈ N0, and continuous fu... |

119 | Curvelet-Wavelet Regularized Split Bregman Iteration for Compressed Sensing - Plonka, Ma - 2009 |

118 |
A Two Parameter Generalization of Lions’ Nonoverlapping Domain Decomposition Method for Linear Elliptic PDEs
- Friedrich
- 2009
(Show Context)
Citation Context |

117 | Error Bounds for Computing the Expectation by Markov Chain Monte Carlo - Rudolf - 2009 |

116 | Accelerated Projected Steepest Descent Method for Nonlinear Inverse Problems with Sparsity Constraints - Teschke, Borries - 2009 |

115 | Variable Subspace Sampling and Multi-level Algorithms
- Müller-Gronbach, Ritter
- 2009
(Show Context)
Citation Context |

115 | Optimally Sparse Image Representation by the Easy Path Wavelet Transform - Plonka, Tenorth, et al. - 2009 |

115 | m-term Approximation and Lizorkin-Triebel Spaces - Best - 2009 |

115 | Dynamical Low-rank Approximation of Tensors - Koch, Lubich - 2009 |

113 | Nonequispaced Hyperbolic Cross Fast Fourier Transform
- Döhler, Kunis, et al.
- 2009
(Show Context)
Citation Context ... 14, 9, 8, 11, 2, 10, 13]. The FFT has been adapted to this thin discretisation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also =-=[5]-=- for a recent generalisation to arbitrary spatial sampling nodes and [4] for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross discrete Fourier ... |

113 | Multilevel Preconditioning for Adaptive Sparse Optimization - Dahlke, Fornasier, et al. - 2009 |

113 | Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise - Lindner, Schilling - 2009 |

111 | A New Hybrid Method for Image Approximation using the Easy Path Wavelet Transform - Plonka, Tenorth, et al. - 2009 |

111 | An Error Analysis of the Multi-configuration Timedependent Hartree Method of Quantum Dynamics - Conte, Lubich - 2009 |

110 | Multi-level Monte Carlo Algorithms for - Hickernell, Müller-Gronbach, et al. - 2009 |

110 | Preconditioning stochastic Galerkin saddle point systems - Powell, Ullmann |

89 | A combination technique for the solution of sparse grid problems - Griebel, Schneider, et al. - 1992 |

87 |
Sparse Grids, Parallel Algorithms for partial differential equations
- Zenger
- 1991
(Show Context)
Citation Context |

38 |
Approximations of functions with bounded mixed derivative,
- Temlyakov
- 1986
(Show Context)
Citation Context |

22 |
A discrete Fourier transform scheme for Boolean sums of trigonometric operators
- Baszenski, Delvos
- 1989
(Show Context)
Citation Context |

21 | 2007): Smolyak’s algorithm, sampling on sparse grids and function spaces of dominating mixed smoothness
- Sickel, Ullrich
(Show Context)
Citation Context |

21 | Data mining with sparse grids - Garcke, Griebel, et al. |

19 |
Boolean Methods in Interpolation and Approximation
- Delvos, Schempp
- 1989
(Show Context)
Citation Context ...2piikx)k∈Ĝj ,x∈Gj , where F j := (e2piikx)x∈Gj ,k∈Ĝj = F j1 ⊗ . . .⊗ F jd denotes the ordinary Fourier matrix. Next, we turn to the trigonometric interpolation on the sparse grid, see the monograph =-=[3]-=- for an introduction. In what follows, the interpolation operator allows for a Boolean sum decomposition which is used for analysing the associated Fourier matrix. For d ∈ N, n ∈ N0, and continuous fu... |

14 |
Fourier transform on sparse grids: code design and application to the time dependent Schrödinger equation on sparse grids. Computing 80
- Gradinaru
- 2007
(Show Context)
Citation Context |

14 |
Fouriertransformation auf dünnen Gittern mit hierarchischen Basen
- Hallatschek
- 1992
(Show Context)
Citation Context |

6 |
A class of function spaces and interpolation on sparse grids
- Sprengel
(Show Context)
Citation Context |

5 |
Interpolation on sparse grids and tensor products of Nikol’skijBesov spaces
- Sickel, Sprengel
- 1999
(Show Context)
Citation Context |

2 |
Matlab toolbox for the nonequispaced hyperbolic cross FFT. http://www.tu-chemnitz.de/~lkae/nhcfft/nhcfft.php
- NHCFFT
- 2009
(Show Context)
Citation Context ...isation as hyperbolic cross fast Fourier transform (HCFFT), which uses Cd2nnd floating point operations, in [1, 7, 6], see also [5] for a recent generalisation to arbitrary spatial sampling nodes and =-=[4]-=- for the associated Matlab toolbox. In this paper, we consider the numerical stability of the hyperbolic cross discrete Fourier transform, which of course limits the stability of a particular and pote... |

2 | Some error estimates for periodic interpolation of functions from Besov spaces
- Sickel, Sprengel
- 1998
(Show Context)
Citation Context |