# Wolfgang Dahmen

#52,468

Most Influential Person Now

German mathematician

## Wolfgang Dahmen 's Degrees

- PhD Mathematics University of Trier

## Why Is Wolfgang Dahmen Influential?

(Suggest an Edit or Addition)According to Wikipedia, Wolfgang Dahmen is a German mathematician working in approximation theory, numerical analysis, and partial differential equations. In 2002, he was awarded the Gottfried Wilhelm Leibniz Prize and in 2011 the Gauss Lectureship. He was also a taekwondo athlete. He has been the Chair of the Society for the Foundations of Computational Mathematics .

## Wolfgang Dahmen 's Published Works

### Published Works

- Compressed sensing and best k-term approximation (2008) (1043)
- Stationary Subdivision (1991) (737)
- Adaptive Finite Element Methods with convergence rates (2004) (570)
- Wavelet and multiscale methods for operator equations (1997) (530)
- Adaptive wavelet methods for elliptic operator equations: Convergence rates (2001) (512)
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods (2010) (436)
- Biorthogonal Spline Wavelets on the Interval—Stability and Moment Conditions (1999) (324)
- Adaptive Wavelet Methods II—Beyond the Elliptic Case (2002) (306)
- Approximation and learning by greedy algorithms (2008) (281)
- Introduction to Model Based Optimization of Chemical Processes on Moving Horizons (2001) (255)
- Wavelets on Manifolds I: Construction and Domain Decomposition (1999) (233)
- Using the refinement equation for evaluating integrals of wavelets (1993) (232)
- Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts (2014) (232)
- Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution (1993) (219)
- Stability of Multiscale Transformations. (1995) (215)
- Composite wavelet bases for operator equations (1999) (208)
- On multivariate -splines (1989) (197)
- Local Decomposition of Refinable Spaces and Wavelets (1996) (187)
- Multilevel preconditioning (1992) (186)
- Tree Approximation and Optimal Encoding (2001) (184)
- Harmonic analysis of the space BV. (2003) (174)
- Adaptive Petrov-Galerkin Methods for First Order Transport Equations (2011) (160)
- Adaptivity and variational stabilization for convection-diffusion equations∗ (2012) (148)
- Blossoming begets B -spline bases built better by B -patches (1992) (148)
- Wavelet methods for PDEs — some recent developments (2001) (144)
- A Multigrid Algorithm for the Mortar Finite Element Method (1999) (143)
- Recent Progress in multivariate splines (1983) (141)
- Wavelet approximation methods for pseudodifferential equations: I Stability and convergence (1994) (138)
- Element-by-Element Construction of Wavelets Satisfying Stability and Moment Conditions (1999) (137)
- Biorthogonal Wavelet Expansions (1997) (131)
- Translates of multivarlate splines (1983) (131)
- Stable multiscale bases and local error estimation for elliptic problems (1997) (129)
- Compression Techniques for Boundary Integral Equations - Asymptotically Optimal Complexity Estimates (2006) (129)
- Biorthogonal Multiwavelets on the Interval: Cubic Hermite Splines (2000) (127)
- DOUBLE GREEDY ALGORITHMS: REDUCED BASIS METHODS FOR TRANSPORT DOMINATED PROBLEMS ∗ (2013) (110)
- Adaptive Wavelet Schemes for Nonlinear Variational Problems (2003) (109)
- Wavelets with Complementary Boundary Conditions — Function Spaces on the Cube (1998) (105)
- Adaptive Wavelet Methods for Saddle Point Problems - Optimal Convergence Rates (2002) (103)
- Multiresolution schemes for conservation laws (2001) (96)
- Universal Algorithms for Learning Theory Part I : Piecewise Constant Functions (2005) (93)
- Multidimensional Spline Approximation (1980) (91)
- Multiresolution analysis and wavelets on S2 and S3 (1995) (91)
- The number of solutions to linear diophantine equations and multivariate splines (1988) (91)
- Adaptive Wavelet Schemes for Elliptic Problems - Implementation and Numerical Experiments (2001) (89)
- Compressed Sensing and Electron Microscopy (2010) (88)
- Nonlinear functionals of wavelet expansions – adaptive reconstruction and fast evaluation (2000) (88)
- Multiscale Wavelet Methods for Partial Differential Equations (1997) (88)
- Compression Techniques for Boundary Integral Equations - Optimal Complexity Estimates (2006) (85)
- Fast high-dimensional approximation with sparse occupancy trees (2011) (85)
- Computation of Curves and Surfaces (1990) (83)
- On the local linear independence of translates of a box spline (1985) (83)
- Approximation Classes for Adaptive Methods (2002) (81)
- Subdivision algorithms for the generation of box spline surfaces (1984) (81)
- Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations (1997) (80)
- Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method (2003) (78)
- Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations (2013) (77)
- On the Linear Independence of Multivariate B-Splines, I. Triangulations of Simploids (1982) (76)
- Multiscale decompositions on bounded domains (2000) (75)
- Optimized imaging using non-rigid registration (2014) (74)
- Data Assimilation in Reduced Modeling (2015) (73)
- On the solution of certain systems of partial difference equations and linear dependence of translates of box splines (1985) (68)
- Cubicoids: modeling and visualization (1993) (64)
- Subdivision algorithms converge quadratically (1986) (59)
- On Multivariate B-Splines (1980) (59)
- Compactly supported fundamental functions for spline interpolation (1988) (58)
- On multivariate E-splines☆ (1989) (56)
- Smooth piecewise quadric surfaces (1989) (56)
- Sparse Evaluation of Compositions of Functions Using Multiscale Expansions (2003) (54)
- Multiscale and Wavelet Methods for Operator Equations (2003) (54)
- Multiscale Methods for Pseudo-Differential Equations on Smooth Closed Manifolds (1994) (54)
- Wavelets in Numerical Analysis (2005) (53)
- Some remarks on multiscale transformations, stability, and biorthogonality (1994) (51)
- On the approximation order from certain multivariate spline spaces (1984) (50)
- Adaptive methods for boundary integral equations: Complexity and convergence estimates (2007) (49)
- Vision-based control of micro-air-vehicles: progress and problems in estimation (2004) (49)
- On the regularization of dynamic data reconciliation problems (2002) (47)
- A cascadic multigrid algorithm for the Stokes equations (1999) (46)
- Banded matrices with banded inverses, II: Locally finite decomposition of spline spaces (1993) (46)
- Tensor-Sparsity of Solutions to High-Dimensional Elliptic Partial Differential Equations (2014) (45)
- Approximation of High-Dimensional Rank One Tensors (2014) (43)
- Adaptive Wavelet Methods for Linear-Quadratic Elliptic Control Problems: Convergence Rates (2005) (43)
- Adaptive Wavelet Methods : Basic Concepts and Applications to the Stokes Problem (2002) (42)
- Numerical simulation of transpiration cooling through porous material (2014) (42)
- C 1 -hierarchical bases (1994) (41)
- A wavelet Galerkin method for the stokes equations (1996) (40)
- Orthogonal Matching Pursuit Under the Restricted Isometry Property (2015) (38)
- Parametric PDEs: sparse or low-rank approximations? (2016) (38)
- Poisson noise removal from high-resolution STEM images based on periodic block matching (2015) (38)
- Stability Estimates of the Mortar Finite Element Method for 3-Dimensional Problems (2007) (36)
- Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition (2001) (36)
- Wavelet Least Squares Methods for Boundary Value Problems (2001) (36)
- Universal Algorithms for Learning Theory. Part II: Piecewise Polynomial Functions (2007) (36)
- Smooth Refinable Functions and Wavelets Obtained by Convolution Products (1995) (36)
- A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method (2008) (36)
- Continuous refinement equations and subdivision (1993) (36)
- On the Linear Independence of Multivariate B-Splines. II: Complete Configurations (1983) (35)
- Numerical boundary layer investigations of transpiration-cooled turbulent channel flow (2015) (35)
- Classification algorithms using adaptive partitioning (2014) (34)
- Multivariate B-Splines — Recurrence Relations and Linear Combinations of Truncated Powers (1979) (33)
- Adaptive eigenvalue computation: complexity estimates (2007) (33)
- Parametric multi-block grid generation and application to adaptive flow simulations (2007) (33)
- Convexity and Bernstein-Bézier Polynomials (1991) (32)
- Exact Riemann solution for the Euler equations with nonconvex and nonsmooth equation of state (2005) (32)
- Instance optimal decoding by thresholding in compressed sensing (2008) (32)
- Adaptive Wavelet Techniques in Numerical Simulation (2004) (31)
- Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods Part I: Geometrically Conforming Meshes (2013) (30)
- Adaptive Low-Rank Methods: Problems on Sobolev Spaces (2014) (30)
- Some remarks on ridge functions (1987) (30)
- Convexity preserving interpolation and Powell-Sabin elements (1992) (29)
- Multiscale methods for pseudodifferential equations (1996) (28)
- Reduced Basis Greedy Selection Using Random Training Sets (2018) (26)
- Towards Multiscale Dynamic Data Reconciliation (1998) (26)
- On the convergence rates of subdivision algorithms for box spline surfaces (1985) (24)
- On the stability of DPG formulations of transport equations (2015) (24)
- Operator equations, multiscale concepts and complexity (1995) (24)
- Super-Resolution Image Reconstruction by Nonlocal Means Applied to High-Angle Annular Darkfield Scanning Transmission Electron Microscopy (HAADF-STEM) (2009) (23)
- Optimal Reduced Model Algorithms for Data-Based State Estimation (2019) (22)
- High-precision scanning transmission electron microscopy at coarse pixel sampling for reduced electron dose (2015) (22)
- On the Theory and Application of exponential splines (1987) (22)
- Adaptive approximation by multivariate smooth splines (1982) (21)
- On the optimal approximation rates for criss-cross finite element spaces (1984) (21)
- Approximation theory VII (1994) (21)
- Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts (2001) (20)
- A factorization theorem for banded matrices (1981) (20)
- Characterization of Local Strict Convexity Preserving Interpolation Methods by C1 Functions (1994) (19)
- HOW TO BEST SAMPLE A SOLUTION MANIFOLD (2015) (19)
- On limits of multivariateB-splines (1981) (19)
- Multilevel preconditioners for the interior penalty discontinuous Galerkin method II- Quantitative studies (2008) (19)
- Two-Level-Split Decomposition of Anisotropic Besov Spaces (2010) (19)
- Adaptive Approximation of Curves (2004) (18)
- Local Dimension of Piecewise Polynomial Spaces, Syzygies, and Solutions of Systems of Partial Differential Equations (1990) (18)
- Approximation by linear combinations of multivariate B-splines (1981) (18)
- On Wachspress quadrilateral patches (2000) (18)
- Fast computation tools for adaptive wavelet schemes (2005) (17)
- Fast computation of adaptive wavelet expansions (2007) (16)
- Line average algorithm: A method for the computer generation of smooth surfaces (1985) (16)
- Scattered data interpolation by bivariate C1-piecewise quadratic functions (1990) (16)
- Multiscale methods for the solution of the Helmholtz and Laplace equations (1997) (16)
- On the Solvability of Certain Systems of Linear Difference Equations (1981) (16)
- Computation of inner products of multivariate B-splines (1981) (15)
- MATRIX EXTENSION WITH SYMMETRY AND APPLICATIONS TO SYMMETRIC ORTHONORMAL COMPLEX M-WAVELETS (2009) (15)
- A conjecture of M. Golomb on optimal and nearly-optimal linear approximation (1974) (15)
- Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012) (15)
- Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations (2001) (15)
- Convergence of Adaptive Wavelet Methods for Goal-Oriented Error Estimation (2006) (15)
- Multilevel preconditioning for partition of unity methods: some analytic concepts (2007) (14)
- Grid refinement in multiscale dynamic optimization (2000) (14)
- Tree Approximation and Encoding (1999) (14)
- Best approximation by piecewise polynomials with variable knots and degrees (1979) (14)
- Polynomials as linear combinations of multivariateB-splines (1979) (14)
- Algebraic Multigrid Methods and the Schur Complement (1989) (14)
- On Stationary Subdivision And the Construction of Compactly Supported Orthonormal Wavelets (1990) (13)
- Modeling Nanoscale Imaging in Electron Microscopy (2012) (13)
- Numerical simulation of cooling gas injection using adaptive multiresolution techniques (2013) (13)
- An adaptive nested source term iteration for radiative transfer equations (2018) (13)
- Riemann Problem for the Euler Equation with Non-Convex Equation of State including Phase Transitions (2005) (13)
- Convexity and Bernstein polynomials on k -simploids (1990) (13)
- Effective Boundary Conditions: A General Strategy and Application to Compressible Flows Over Rough Boundaries (2017) (13)
- Decomposition of refinable spaces and applications to operator equations (1993) (12)
- On Multivariate Splines, Matroids, and the Ext-Functor (1996) (12)
- A multiscale method for the double layer potential equation on a polyhedron. (2005) (12)
- Adaptive application of operators in standard representation (2006) (12)
- Numerical schemes and well-posedness in nonlinear aeroelasticity (2002) (12)
- Some results on box splines (1984) (11)
- Efficient Resolution of Anisotropic Structures (2014) (11)
- Multiscale Concepts for Moving Horizon Optimization (2001) (11)
- Legendre-Gauss-Lobatto grids and associated nested dyadic grids (2013) (11)
- An adaptive multiscale method for real-time moving horizon optimization (2000) (10)
- Local spline interpolation schemes in one and several variables (1989) (10)
- Numerical Algorithms for Least Squares Approximation by Multivariate B-Splines (1982) (10)
- Adaptive anisotropic Petrov-Galerkin methods for first order transport equations (2016) (9)
- Nonlinear reduced models for state and parameter estimation (2020) (9)
- The Mortar element method revisited – What are the right norms ? (2001) (9)
- A hierarchical approach to force field calculations through spline approximations (1994) (9)
- Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm (2010) (9)
- Algebraic properties of discrete box splines (1987) (9)
- Numerical simulation of cooling gas injection using adaptive multiscale techniques (2010) (9)
- On Linear Dependence Relations for Integer Translates of Compactly Supported Distributions (1991) (9)
- Inverse Inequalities on Non � Quasiuniform Meshes and Application to the Mortar Element Method W � Dahmen (2003) (8)
- On Well-Posedness and Modelling for Nonlinear Aeroelasticity (2003) (8)
- On an Adaptive Multigrid Solver for Convection-Dominated Problems (2001) (8)
- A Unified Approach to the Modeling of Airplane Wings and Numerical Grid Generation Using B-Spline Representations (2010) (8)
- Subdivision algorithms—recent results, some extensions and further developments (1987) (7)
- Adaptive Strategies for Transport Equations (2018) (7)
- Best approximation with exponential orders and intermediate spaces (1976) (7)
- A semigroup approach to the numerical solution of parabolic differential equations (2005) (6)
- ON THE STABILITY OF NONLINEAR CONSERVATION LAWS IN THE HAUSDORFF METRIC (2005) (6)
- State Estimation - The Role of Reduced Models (2020) (6)
- "Push-the-Error" Algorithm for Nonlinear n-Term Approximation (2006) (6)
- Wavelet Least Square Methods for Boundary Value Problems (1999) (6)
- NUMERICAL SIMULATION OF TRANSPIRATION COOLING WITH A MIXTURE OF THERMALLY PERFECT GASES (2013) (6)
- Effective boundary conditions for compressible flows over rough boundaries (2015) (6)
- APPROXIMATION BY SMOOTH MULTIVARIATE SPLINES ON NON-UNIFORM GRIDS (1980) (5)
- On entire functions of affine lineage (1982) (5)
- Asymptotically optimal sampling schemes for periodic functions (1986) (5)
- Trigonometric approximation with exponential error orders (1977) (5)
- A taste of compressed sensing (2007) (5)
- On monotone extensions of boundary data (1991) (5)
- Error controlled regularization by projection. (2006) (5)
- Multiscale Problems and Methods in Numerical Simulations: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 9-15, 2001 (2004) (5)
- Towards a fictitious domain method with optimally smooth solutions (2005) (5)
- Adaptive multiresolution finite volume discretization of the Variational Multiscale Method. General Framework (2011) (5)
- On factorization of biinfinite totally positive block Toeplitz matrices (1986) (5)
- Accuracy controlled data assimilation for parabolic problems (2021) (4)
- Best approximation and de la Vallée-Poussin sums (1978) (4)
- Multigrid and Multiscale Decompositions (1997) (4)
- Some Remarks on Multivariate B-Splines (1982) (4)
- Trigonometric approximation with exponential error orders. II. Properties of asymptotically optimal processes: Impossibility of arbitrarily good error estimates (1979) (4)
- The characterization problem for best approximation with exponential error orders and evaluation of entropy (1977) (4)
- On Fictitious Domain Formulations for Maxwell's Equations (2003) (4)
- Parallel and Adaptive Methods for Fluid-Structure-Interactions (2010) (4)
- Multiscale methods for pseudodifferential equations on manifolds (1995) (4)
- Robust Preconditioners for DG-Discretizations with Arbitrary Polynomial Degrees (2012) (4)
- Universal Piecewise Polynomial Estimators for Machine Learning (2006) (4)
- Orthogonal Matching Pursuit Under the Restricted Isometry Property (2016) (4)
- Compositional Sparsity, Approximation Classes, and Parametric Transport Equations (2022) (4)
- Infinite dimensional stabilization of convection dominated problems (2013) (4)
- Multiscale Wavelet Methods for Partial Differential Equations, Volume 6 (1997) (3)
- Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations (2014) (3)
- Adaptive Multiscale Methods for Flow Problems: Recent Developments (2010) (3)
- Approximation of High-Dimensional Rank One Tensors (2013) (3)
- High-order methods for convection dominated nonlinear problems using multilevel techniques (2011) (3)
- Stationary Subdivision, Fractals and Wavelets (1990) (3)
- Nested dyadic grids associated with Legendre–Gauss–Lobatto grids (2015) (3)
- Asymptotically Optimal Linear Approximation Processes and a Conjecture of Golomb (1974) (3)
- Combinatorial Aspects of Multivariate Splines (1985) (3)
- Adaptive Wavelet S hemes for Ellipti Problems { Implementation and Numeri al Experiments (1999) (3)
- BLOSSOMING BEGETS ß-SPLINE BASES BUILT BETTER BY ß-PATCHES (2010) (3)
- Numerical simulation of effusion cooling through porous media (2013) (2)
- A Wavelet-Galerkin Method applied to Separation Processes (1996) (2)
- A basis for certain spaces of multivariate polynomials and exponentials (1990) (2)
- Numerical investigation of transpiration cooling with uniformly and non-uniformly simulated injection (2017) (2)
- Regularization of Dynamic Data Reconciliation Problems by Projection 1 (2000) (2)
- Effective Boundary Conditions for Turbulent Compressible Flows over a Riblet Surface (2016) (2)
- ADAPTIVE EIGENVALUE COMPUTATION FOR ELLIPTIC OPERATORS (2010) (2)
- On the piecewise structure of discrete box splines (1986) (2)
- Iterative Multiscale Methods for Process Monitoring (2001) (1)
- Non-local denoising and unsupervised quantitative analysis in scanning transmission electron microscopy (2017) (1)
- Numerical investigation of transpiration cooling effects on turbulent boundary layers (2015) (1)
- Adaptive source term iteration : a stable formulation for radiative transfer (2019) (1)
- Tree Approximation and Optimal Encoding 1 (1999) (1)
- Effective boundary conditions for compressible flows over a rough surface : Isothermal case (2015) (1)
- Nonlinear Reduced DNN Models for State Estimation (2021) (1)
- Multiscale Techniques — Some Concepts and Perspectives (1995) (1)
- Efficient numerical methods for L0-norm related minimizations (2017) (0)
- STOCHASTIC PDE’S: A MULTISCALE MODELLING CONCEPT (2008) (0)
- CA Special Issue on Neural Network Approximation (2021) (0)
- 1. g From finite differences to finite elements: A short history of numerical analysis of partial differential (2003) (0)
- Optimal Decoding by Thresholding in Compressed Sensing (2008) (0)
- Optimal Geometry Representations for High-Quality Visualization (1999) (0)
- Nested dyadic grids associated with Legendre–Gauss–Lobatto grids (2014) (0)
- Computation and Learning in High Dimensions (2022) (0)
- On the stability of conservation laws in the Hausdorff metric (2005) (0)
- Measuring Surface Atom Bond Length Contraction in Au and Pt Nanoparticles Using High-Precision STEM Imaging (2013) (0)
- A Discontinuous Petrov-Galerkin method for the transport equation (2016) (0)
- ASYMPTOTICALLY OPTIMAL LINEAR APPROXIMATION PROCESSES (1974) (0)
- Adaptive Approximation by Multivariate (1982) (0)
- Tensor-Sparsity of Solutions to High-Dimensional Elliptic Partial Differential Equations (2015) (0)
- Data and Models (2018) (0)
- An Adapted Divergence-Free Wavelet Basis for the Simulation of Wall-Bounded Flows (2001) (0)
- The volume of restricted moment spaces (1989) (0)
- DIVERGENCE-FREE WAVELET ANALYSIS OF TURBULENTFLOWSCEM (2002) (0)
- Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity (2019) (0)
- Reduced order modeling for elliptic problems with high contrast diffusion coefficients (2023) (0)
- Data Compression, Process Optimization, Aerodynamics: A Tour Through the Scales (2010) (0)
- Correction to: Preface (2021) (0)
- HIGH DIMENSIONAL APPROXIMATION SEMINAR CONCENTRATION PHENOMENA (2008) (0)
- N A ] 1 F eb 2 02 0 State Estimation-The Role of Reduced Models (2020) (0)
- Numerical investigation of the interface between porous media and a transpiration-cooled turbulent channel ﬂow (2016) (0)
- AND LINEAR COMBINATIONS OF TRUNCATED POWERS (1979) (0)
- Adaptive Finite Element Methods with Convergen eRates (2010) (0)
- HIGH DIMENSIONAL APPROXIMATION SEMINAR INTRODUCTION (2008) (0)
- Computational Harmonic Analysis Organizing Committee Conference Secretary General Information Lecture Theatres Foreign Currency Exchange Email/fax Sightseeing Trip Non-uniform Sampling and Reconstruction in Shift-invariant Spaces with Applications to Signal and Image Processing Multiwavelet Transfor (0)
- Least squares solvers for ill-posed PDEs that are conditionally stable (2022) (0)
- Wavelet and Multiscale Methods (2004) (0)
- Correction to: Preface (2021) (0)
- A Cascade Algorithm for the Stokes Equations (2007) (0)
- Hybrid compression of boundary element matrices for high-frequency Helmholtz problems (2018) (0)
- Fast Highdimensional Approximation with Sparse Occupancy Trees (Preprint) (2010) (0)
- Solving PDEs with Incomplete Information (2023) (0)
- Compressed sensing approaches for novel 3 D imaging modes in the TEM 16 : 30 – 17 : 00 (2014) (0)
- Workshop on Applied Linear Algebra in Honor of Ludwig Elsner Bielefeld Hh Orsaal H15 (1999) (0)
- CA Special Issue on Neural Network Approximation (2021) (0)
- AND BEST k -TERM APPROXIMATION (2008) (0)

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## Other Resources About Wolfgang Dahmen

## What Schools Are Affiliated With Wolfgang Dahmen ?

Wolfgang Dahmen is affiliated with the following schools: