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Inhalt des Dokuments


M. Geist, Ph. Petersen, M. Raslan, R. Schneider, G. Kutyniok
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
arxiv: https://arxiv.org/abs/2004.12131

G. Kutyniok, M. Raslan, Ph. Petersen, R. Schneider
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
arxiv: https://arxiv.org/abs/1904.00377

K. Fackeldey, M. Oster, L. Sallandt, R. Schneider
Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format
arxiv: https://arxiv.org/abs/2010.04465

M. Eigel, Ph. Trunschke, R. Schneider
Convergence bounds for empirical nonlinear least-squares
arxiv: https://arxiv.org/abs/2001.00639

M. Eigel, M. Marschall, M. Pfeffer, R. Schneider
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
Numerische Mathematik, Vol. 145, (2020) pp. 655-692
DOI: https://link.springer.com/article/10.1007%2Fs00211-020-01123-1

R. Schneider, F. Faulstich, A. Laestadius, S. Kvaal, O. Legaza
Analysis of the coupled-cluster method tailored by tensor-network states in quantum chemistry
SIAM Journal on Numerical Analysis, Vol.57 (6), (2019), pp. 2579-2607
DOI: https://epubs.siam.org/doi/10.1137/18M1171436

M. Eigel, R. Schneider, Ph. Trunschke, S. Wolf
Variational Monte Carlo - Bridging Concepts of Machine Learning and High Dimensional Partial Differential Equations
Advances in Computational Mathematics, Vol. 45, (2019) pp. 2503-2532
DOI: https://link.springer.com/article/10.1007/s10444-019-09723-8

F. Faulstich, M. Máté, A. Laestadius, M. Csirik, L. Veis, A. Antalik, J. Brabec, R. Schneider, J. Pittner, S. Kvaal, O. Legeza
Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer
Journal of Chemical Theory and Computation, Vol. 15 (4), (2019), pp. 2206-2220
DOI: https://pubs.acs.org/doi/10.1021/acs.jctc.8b00960

M. Eigel, J. Neumann, R. Schneider, S. Wolf
Risk averse stochastic structural topology optimization
Computational Methods in Applied Mechanics and Engineering, Vol. 334 (2018), pp. 470-482
DOI: https://doi.org/10.1016/j.cma.2018.02.003

M. Eigel, M. Marschall, R. Schneider
Sampling-free Bayesian Inversion with adaptive hierarchical tensor representations
Inverse Problems, Vol. 34 (2018), No. 3, pp. 29
DOI: 10.1088/1361-6420/aaa998

B. Huber, R. Schneider, S. Wolf
A randomized tensor train singular value decomposition
Compressed sensing and its applications, Applied and Numerical Harmonic Analysis (2017), pp. 261-290
DOI: https://doi.org/10.1007/978-3-319-69802-1_9
arxiv: arXiv:1710.08513

H. Harbrecht, R. Schneider
A note on multilevel based error estimation
Computational Methods in Applied Mathematics, Vol. 16 (2016), No. 3, pp. 447-458
DOI: https://doi.org/10.1515/cmam-2016-0013

H. Rauhut, R. Schneider, Ž. Stojanac
Low rank tensor recovery via iterative hard thresholding
Linear Algebra and its Applications, Vol. 523 (2017), pp. 220-262
DOI: https://doi.org/10.1016/j.laa.2017.02.028 
arXiv: arXiv:1602.05217v1

F. Nüske, R. Schneider, F. Vitalini, F. Noé
Variational Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems
Journal of Chemical Physics, Vol. 144 (2016), No. 5, pp. 1-14
DOI: https://doi.org/10.1063/1.4940774
(link to journal) (PDF)

M. Eigel, M. Pfeffer, R. Schneider
Adaptive Stochastic Galerkin FEM with Hierarchical Tensor Representations

Numerische Mathematik, Vol. 136 (2016), pp. 1-39
DOI: https://doi.org/10.1007/s00211-016-0850-x
(link to journal) (PDF)

M. Bachmayr, R. Schneider, A. Uschmajew
Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations
Foundations of Computational Mathematics, Vol. 16 (2016), No. 6, pp.1423-1472
DOI: https://doi.org/10.1007/s10208-016-9317-9
(link to journal) (PDF)

R. Schneider, M. Bachmayr
Iterative methods based on soft thresholding of hierarchical tensors
Foundations of Computational Mathematics, (2016), pp. 1-47
DOI: 10.1007/s10208-016-9314-z
arXiv: 1501.07714

H. Rauhut, R. Schneider, Ž. Stojanac
Tensor completion in hierarchical tensor representations. Compressed sensing and its applications
Applied Numerical Harmonic Analysis, (2015), pp. 419-450
DOI: https://doi.org/10.1007/978-3-319-16042-9_14
arXiv: arXiv:1404.3905v2

R. Schneider, A. Uschmajew
Convergence results for projected line-search methods on varieties of low-rank matrices via Łojasiewicz inequality
SIAM Journal on Optimization, Vol. 25 (2015), No. 1, pp. 622-646
DOI: https://doi.org/10.1137/140957822

96) H. Chen, R. Schneider
Error estimates of some numerical atomic orbitals in molecular simulations
Communications in Computational Physics, Vol. 18 (2015), No. 1, pp. 125-146
DOI: https://doi.org/10.4208/cicp.170414.231214a

R. Schneider, Ö. Legeza, Th. Rohwedder, S. Szalay
Tensor Product Approximation (DMRG) and Coupled Cluster Method in Quantum Chemistry
Mathematical Physics Studies, 2014, pp. 53-76
DOI: 10.1007/978-3-319-06379-9_3
arXiv: arXiv:1310.2736v1

R. Schneider, H. Chen
Numerical analysis of augmented plane wave methods for full-potential electronic structure calculations
ESAIM Mathematical Modelling and Numerical Analysis, Vol. 49 (2015), no. 3, pp. 755–785
DOI: http://dx.doi.org/10.1051/m2an/2014052

M. Bachmayr, H. Chen, R. Schneider
Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry
Numerical Mathematics, Vol. 128 (2014), No. 1, pp. 137-165
DOI: https://doi.org/10.1007/s00211-014-0605-5

S. Szalay, M. Pfeffer, V. Murg, G. Barcza, F. Verstraete, R. Schneider, O. Legeza
Tensor product methods and entaglement optimization for ab initio quantum chemistry
International Journal of Quantum Chemistry, Vol. 115 (2015), pp. 1342-1391
DOI: https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.24898
arXiv: arXiv:1412.5829v1

R. Schneider, W. Hackbusch
Tensor Spaces and Hierarchical Tensor Representations
Lecture Notes in Computational Science and Engineering, Vol. 102 (2014), pp. 237-259
DOI: 10.1007/978-3-319-08159-5_12

R. Schneider, A. Uschmajew
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces
Journal of Complexity, Vol. 30 (2014), No. 2, pp. 56-71
DOI: https://doi.org/10.1016/j.jco.2013.10.001

Th. Rohwedder, R. Schneider
Error estimates for the coupled cluster method
ESAIM Mathematical Modelling and Numerical Analysis, Vol. 47 (2013), No. 6, pp. 1553-1582
DOI: http://dx.doi.org/10.1051/m2an/2013075

Ch. Lubich, Th. Rohwedder, R. Schneider, B. Vandereycken
Dynamical approximation by hierarchical Tucker and tensor-train tensors
SIAM Journal on Matrix Analysis  and Applications, Vol. 34 (2013), No. 2, pp. 470-494
DOI: https://doi.org/10.1137/120885723

V. Khoromskaia, B. N. Khoromskij, R. Schneider
Tensor-structured factorized calculation of two-electron integrals in a general basis
SIAM Journal on Scientific Computing, Vol. 35 (2013), No. 2, pp. A987-A1010
DOI: https://doi.org/10.1137/120884067

M. Espig, W. Hackbusch, Th. Rohwedder, R. Schneider
Variational calculus with sums of elementary tensors of fixed rank
Numerische Mathematik, Vol. 122 (2012), No. 3, pp. 469-488
DOI: https://doi.org/10.1007/s00211-012-0464-x

H.-J. Flad, R. Schneider
S*-compressilibity of discrete Hartree-Fock equations
ESAIM Mathematical Modelling and Numerical Analysis, Vol. 46 (2012), No. 5, pp. 1055-1080
DOI: https://doi.org/10.1051/m2an/2011077

S. Holtz, Th. Rohwedder, R. Schneider
The alternating linear scheme for tensor optimization in the tensor train format
SIAM Journal on Scientific Computing, Vol. 34 (2012), No. 2, pp. A683-A713
DOI: https://doi.org/10.1137/100818893

H. Harbrecht, M. Peters, R. Schneider
On the low-rank approximation by the pivoted Cholesky decomposition
Applied Numerical Mathematics, Vol. 62 (2012), No. 4, pp. 428-440
DOI: https://doi.org/10.1016/j.apnum.2011.10.001

S. Holtz, Th. Rohwedder, R. Schneider
On manifolds of tensors of fixed TT-rank
Numerische Mathematik, Vol. 120 (2012), No. 4, pp. 701-731
DOI: https://doi.org/10.1007/s00211-011-0419-7

M. Espig, W. Hackbusch, St. Handschuh, R. Schneider
Optimization problems in contracted tensor networks
Computing and Visualization in Science, Vol. 14 (2011), No. 6, pp. 271-285
DOI: https://doi.org/10.1007/s00791-012-0183-y

V. Khoromskaia, B. Khoromskij, R. Schneider
QTT representation of the Hartree and exchange operators in electronic structure calculations
Computational Methods in Applied Mathematics, Vol. 11 (2011), no. 3, pp. 327-341
DOI: https://doi.org/10.2478/cmam-2011-0018

Th. Rohwedder, R. Schneider
An analysis for the DIIS acceleration method used in quantum chemistry calculations
Journal of Mathematical Chemistry, Vol. 49 (2011), No. 9, pp. 1889-1914
DOI: https://doi.org/10.1007/s10910-011-9863-y

H.-J. Flad, G. Harutyunyan, R. Schneider, B-W. Schulze
Explicit Green operators for quantum mechanical Hamiltonians. I. The hydrongen atom.
Manuscripta Mathematica, Vol. 135 (2011), No. 3-4, pp. 497-519
DOI: https://doi.org/10.1007/s00229-011-0429-x
arXiv: arXiv:1003.3150v1

Th. Rohwedder, R. Schneider, A. Zeiser
Perturbed preconditioned inverse iteration for operator eigenvalue problems with application at adaptive wavelet discretization
Advances in Computational Mathematics, Vol. 34 (2011), No. 1, pp. 43-66
DOI: 10.1007/s10444-009-9141-8
arXiv: arXiv:0708.0517v2

H.-J. Flad, W. Hackbusch, B. N. Khoromskij, R. Schneider
Concepts of data-sparse tensor-product approximation in many-particle modelling
Matrix methods: theory, algorithms and applications, pp. 313-347, World Sci. Publ., Hackensack, NJ, 2010
DOI: https://doi.org/10.1142/9789812836021_0020

R. Schneider, O. Reichmann, Ch. Schwab
Wavelet solution of variable order pseudodifferential equations
Calcolo, Vol. 47 (2010), No. 2, pp. 65-101
DOI: https://doi.org/10.1007/s10092-009-0012-y

R. Schneider, Th. Rohwedder, H.-J. Flad
Adaptive Methods in Quantum Chemistry
Zeitschrift für Physikalische Chemie, Springer, Vol. 224 (2010), Nr. 3-4, pp. 651-669
DOI: DOI: 10.1524/zpch.2010.6129}

H. Harbrecht, R. Schneider
Rapid solution of boundary integral equations by wavelet Galerkin schemes
Multiscale, nonlinear and adaptive approximation, pp. 249-294, Springer, Berlin, 2009
DOI: 10.1007/978-3-642-03413-8_8

R. Schneider
Analysis of the projected coupled cluster method in electronic structure calculation (revised version)
Numerische Mathematik, Vol. 113 (2009), No. 3, pp. 433-471
DOI: https://doi.org/10.1007/s00211-009-0237-3

R. Schneider, Th. Rohwedder, J. Blauert
Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
Journal of Computational Mathematics (2009), Vol. 27, No. 2-3, pp. 360-387
arXiv: arXiv:0805.1190v1

J. Sielk, H.F. von Horsten, F. Krüger, R. Schneider, B. Hartke
Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation
Physical Chemistry Chemical Physics 11 (2009) no. 3, pp. 463-475
DOI: 10.1039/b814315c

H.-J. Flad, W. Hackbusch, B. Khoromskij, R. Schneider
Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling, Matrix Methods: Theory, Algorithms and Applications
Dedicated to the Memory of Gene Golub (2009), World Scientific
DOI: https://doi.org/10.1142/9789812836021_0020

H.-J. Flad, R. Schneider, B. W. Schulze
Asymptotic regularity of solutions to Hartree-Fock equations with Coulomb potential
Mathematical Methods in the Applied Sciences, Vol. 31 (2008), no. 18, pp. 2172-2201
DOI: 10.1002/mma.1021

W. Dahmen, Th. Rohwedder, R. Schneider, A. Zeiser
Adaptive eigenvalue computation: complexity estimates
Numerische Mathematik, Vol. 110 (2008), no. 3, pp. 277–312
DOI: https://doi.org/10.1007/s00211-008-0159-5

H. Harbrecht, R. Schneider, Ch. Schwab
Multilevel frames for sparse tensor product spaces
Numerische Mathematik, Vol. 110 (2008), no. 2, pp. 199–220
DOI: https://doi.org/10.1007/s00211-008-0162-x

H. Harbrecht, R. Schneider, Ch. Schwab
Sparse second moment analysis for elliptic problems in stochastic domains
Numerische Mathematik, Vol. 109 (2008), no. 3, pp. 385–414
DOI: https://doi.org/10.1007/s00211-008-0147-9

L. Genovese, A. Neelov, St. Goedecker, Th. Deutsch, S. A. Ghasemi, A. Willand, D. Caliste, O. Zilberberg, M. Rayson, A. Bergman, R. Schneider
Daubechies wavelets as a basis set for density functional pseudopotential calculations
Journal of Chemical Physics, Vol. 129, 014109 (2008)
DOI: https://doi.org/10.1063/1.2949547

R. Schneider, T. Weber
Multiscale approximation schemes in electronic structure calculation, in Harmonic, wavelet and p-adic analysis
Eds. N.M. Chuong et al. (2007) World Scientific, pp. 59 –81

M. Gnewuch, R. Lindloh, R. Schneider, A. Srivastav
Cubature formulas for function spaces with moderate smoothness
Journal of Complexity, Vol. 23 (2007), no. 4-6, pp. 828–850
DOI: https://doi.org/10.1016/j.jco.2007.07.002

H.-J. Flad, W. Hackbusch, R. Schneider
Best N-term approximation in electronic structure calculation II. Jastrow factors
ESIAM: Mathematical Modellng and Numerical Analysis, Vol. 41 (2007), no. 2, pp. 261 –279
DOI: https://doi.org/10.1051/m2an:2007016

W. Dahmen, H. Harbrecht, R. Schneider
Adaptive methods for boundary integral equations : complexity and convergence estimates
Mathematics of Computation, Vol. 76 (2007), no. 259, pp. 1243–1274

K. Eppler, H. Harbrecht, R. Schneider
On convergence in elliptic shape optimization
SIAM Journal on Control and Optimization, Vol. 46 (2007), no. 1, pp. 61–83
DOI: https://doi.org/10.1137/05062679X

A. Barinka, W. Dahmen, R. Schneider
Fast computation of adaptive wavelet expansions
Numerische Mathematik, Vol. 105 (2007), no. 4, pp. 549–589
DOI: https://doi.org/10.1007/s00211-006-0050-1

R. Schneider
Adaptive coupled cluster method and CI method for the solution of the electronic Schrödinger equation
Oberwolfach Reports, Vol. 36 (2007), pp. 2133-2136

H. Harbrecht, U. Kähler, R. Schneider
Wavelet matrix compression for boundary integral equations. Parallel algorithms and cluster computing
Lectures Notes in Computational Sciences and Engineering, Vol. 52, Springer, Berlin, 2006, pp. 129–149
DOI: https://doi.org/10.1007/3-540-33541-2_8

R. Schneider, T. Weber
Wavelets for density matrix computation in electronic structure calculation
Applied Numerical Mathematics, Vol. 56 (2006), no. 10-11, pp. 1383–1396
DOI: https://doi.org/10.1016/j.apnum.2006.03.020

R. Schneider, Y. Xu, A. Zhou
An analysis of discontinuous Galerkin methods for elliptic problems
Advances in Computational Mathematics, Vol. 25 (2006), no. 1-3, pp. 259–286
DOI: https://doi.org/10.1007/s10444-004-7619-y

H.-J. Flad, W. Hackbusch, R. Schneider
Best N-term approximation in electronic structure calculations. I. One-electron reduced density matrix
ESIAM: Mathematical Modelling and Numerical Analysis, Vol. 40 (2006), pp. 49–61
DOI: https://doi.org/10.1051/m2an:2006007

W. Dahmen, H. Harbrecht, R. Schneider
Compression techniques for boundary integral equations - asymptotically optimal complexity estimates
SIAM Journal on Numerical Analysis, Vol. 43, No. 6, pp. 2251-2271 (2006)
DOI: https://doi.org/10.1137/S0036142903428852

H. Harbrecht, R. Schneider
Wavelet Galerkin schemes for boundary integral equations - implementation and quadrature
SIAM Journal on Scientific Computing, Vol. 27 (2006), No. 4, pp. 1347-1370
DOI: https://doi.org/10.1137/S1064827503429387

S. Beuchler, R. Schneider, Ch. Schwab
Erratum: Multiresolution weighted norm equivalences and applications
Numerische Mathematik, Vol. 98 (2004), No. 1, pp. 67-97
Numerische Mathematik, Vol. 102 (2005), No. 2, pp. 365-366
DOI: https://doi.org/10.1007/s00211-005-0633-2

R. Schneider, Ch. Schwab
Wavelet FEM for variable order pseudodifferential equations
Submitted to Calcolo. Preprint Nr. 05-10, CAU Kiel (2005)

H. Harbrecht, U. Kähler, R. Schneider
Wavelet Galerkin BEM on unstructured meshes
Computing and Visulization in Science, Vol. 8 (2005), no. 3-4, pp. 189 –199
DOI: https://doi.org/10.1007/s00791-005-0009-2

H. Harbrecht, U. Kähler, R. Schneider
Wavelet Matrix Compression for Boundary Integral Equations
GAMM (Proceedings of the GAMM Conference 2005), Vol. 5, pp. 767-768 (2005)
DOI: https://doi.org/10.1007/3-540-33541-2_8

H. Harbrecht, R. Schneider
Wavelet based fast solution of boundary integral equations
In: Abstract and Applied Analysis (Proceedings of the International Conference in Hanoi, 2002), edited by N.M. Chuong et al., World Scientific Publishing Company (2004), pp. 139-162
DOI: https://doi.org/10.1142/9789812702548_0008

H. Harbrecht, R. Schneider
Biorthogonal wavelet bases for the boundary element method
Mathematische Nachrichten, Vol. 269/270 (2004), pp. 167–188
DOI: https://doi.org/10.1002/mana.200310171

S. Beuchler, R. Schneider, Ch. Schwab
Multiresolution weighted norm equivalences and applications
Numerische Mathematik, Vol. 98 (2004), no. 1, pp. 67–97
DOI: https://doi.org/10.1007/s00211-003-0491-8

H. Harbrecht, M. Konik, R. Schneider
Fully Discrete Wavelet Galerkin Schemes
Engineering Analysis with Boundary Elements Vol. 28, (2004)

M. Randrianarivony, G. Brunnett, R. Schneider
Constructing a diffeomorphism between a trimmed domain and the unit square
December 2003. Preprint SFB393 TU Chemnitz 2003

H. Harbrecht, R. Schneider
Adaptive Wavelet Galerkin BEM
Computational Fluid and Solid Mechanics 2003, Vol. 2, edited by K.J. Bathe, Elsevier, pp. 1982-1986 (2003)
DOI: https://doi.org/10.1016/B978-008044046-0.50486-3

G. N. Gatica, H. Harbrecht, R. Schneider
Least squares methods for the coupling of FEM and BEM
SIAM Journal on Numerical Analysis, Vol. 41 (2003), no. 5, pp. 1974–1995
DOI: https://doi.org/10.1137/S0036142902400664

H. Harbrecht, S. Pereverzev, R. Schneider
Self-regularization by projection for noisy pseudodifferential equations of negative order
Numerische Mathematik, Vol. 95 (2003), no. 1, pp. 123–143
DOI: https://doi.org/10.1007/s00211-002-0417-x

A. Rathsfeld, R. Schneider
On a quadrature algorithm for the piecewise linear collocation applied to boundary integral equations
Mathematical Methods in the Applied Sciences, Vol. 26 (2003), no. 11, pp. 937–979
DOI: https://doi.org/10.1002/mma.408

H. Harbrecht, C. Pérez, F. Paiva, R. Schneider
Multiscale preconditioning for the coupling of FEM-BEM
Numerical Linear Algebra with Applications, Vol. 10 (2003), no. 3, pp. 197–222
DOI: https://doi.org/10.1002/nla.284

H. Harbrecht, F. Paiva, C. Pérez, R. Schneider
Biorthogonal wavelet approximation for the coupling of FEM-BEM
Numerische Mathematik, Vol. 92 (2002), No. 2, pp. 325-356
DOI: https://doi.org/10.1007/s002110100283

W. Dahmen, A. Kunoth, R. Schneider
Wavelet least squares methods for boundary value problems
SIAM Journal on Numerical Analysis, Vol. 39 (2002), No. 6, pp. 1985-2013

H. Harbrecht, R. Schneider
Wavelet Galerkin schemes for 2D-BEM
Problems and methods in mathematical physics (Chemnitz, 1999), pp. 221-260, Operator Theory: Advances and Applications, Vol. 121, Birkhäuser, Basel, 2001
DOI: https://doi.org/10.1007/978-3-0348-8276-7_14

C. Pérez, R. Schneider
Wavelet Galerkin methods for boundary integral equations and the coupling with finite element methods
Wavelet transforms and time-frequency signal analysis, pp. 145-179
Applied Numerical Harmonic Analysis, Birkhäuser Boston, Boston, MA, 2001
DOI: https://doi.org/10.1007/978-1-4612-0137-3_6

W. Dahmen, R. Schneider, Y. Xu
Nonlinear functionals of wavelet expansions - adaptive reconstruction and fast evaluation
Numerische Mathematik, Vol. 86 (2000), No. 1, pp. 49-101
DOI: https://doi.org/10.1007/PL00005403

W. Dahmen, R. Schneider
Wavelets on manifolds. I. Construction and domain decomposition
SIAM Journal on Mathematical Analysis, Vol. 31 (1999), No. 1, pp. 184-230
DOI: https://doi.org/10.1137/S0036141098333451

W. Dahmen, R. Schneider
Composite wavelet bases for operator equations
Mathematics of Computation, Vol. 68 (1999), No. 228, pp. 1533-1567

J. Reinhold, J. Friese, H.-J. Körner, R. Schneider, K. Zeitelhack, H. Geissel, A. Magel, G. Münzenberg, and K. Sümmerer
Projectile fragmentation of 129Xe at Elab=790A MeV
Physical Review C Vol. 58, (1998) No. 1
DOI: https://doi.org/10.1103/PhysRevC.58.247

W. Dahmen, R. Schneider
Wavelets with complementary boundary conditions - function spaces on the cube
Results in Mathematics, Vol. 34 (1998), No. 3-4, pp. 255-293
DOI: https://doi.org/10.1007/BF03322055

R. Schneider
Multiskalen- und Wavelet-Matrixkompression. (German) (Multiscale and wavelet matrix compression). Analysisbasierte Methoden zur effizienten Lösung großer vollbesetzter Gleichungssysteme (Analysis-based methdos for the efficient solution of large nonsparse systems of equations)
Advances in Numerical Methematics, B. G. Teubner, Stuttgart, 1998, 246 pp
ISBN: 3-519-02739-9
DOI: https://doi.org/10.1007/978-3-663-10851-1

W. Dahmen, B. H. Kleemann, S. Prössdorf, R. Schneider
Multiscale methods for the solution of the Helmholtz and Laplace equations
Boundary element topics (Stuttgart, 1995), pp. 189-219, Springer, Berlin, 1997
DOI: https://doi.org/10.1007/978-3-642-60791-2_10

T. von Petersdorff, Ch. Schwab, R. Schneider
Multiwavelets for second-kind integral equations
SIAM Journal on Numerical Analysis, Vol. 34 (1997), no. 6, pp. 2212-2227
DOI: https://doi.org/10.1137/S0036142994272957

St. Dahlke, W. Dahmen, R. Hochmuth, R. Schneider
Stable multiscale bases and local error estimation for elliptic problems. Multilevel Methods (Oberwolfach, 1995)
Applied Numerical Mathematics, Vol. 23 (1997), No. 1, pp. 21-47
DOI: https://doi.org/10.1016/S0168-9274(96)00060-8

B. H. Kleemann, A. Rathsfeld, R. Schneider
Multiscale methods for boundary integral equations and their application to boundary value problems in scattering theory and geodesy.
Boundary elements: implementation and analysis of advanced algorithms (Kiel, 1996), pp. 1-28
Notes on Numerical Fluid mechanics, Vol. 54, Vieweg, Braunschweig, 1996
DOI: https://doi.org/10.1007/978-3-322-89941-5_1

W. Dahmen, B. H. Kleemann, S. Prössdorf, R. Schneider
Multiscale methods for pseudodifferential equations
ICIAM/GAMM 95 (Hamburg, 1995)
ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik, Vol. 76 (1996), suppl. 1, pp. 7-10
DOI: https://doi.org/10.1016/B978-0-08-052084-1.50023-5

W. Dahmen, A. Kunoth, R. Schneider
Operator equations, multiscale concepts and complexity
The mathematics of numerical analysis (Park City, UT, 1995), pp. 225-261
Lectures in Applied Mathematics, Vol. 32, Amer. Math. Soc., Providence, RI, 1996

M. Konik, R. Schneider, G. Steidl
Matrix compression by discrete wavelet transform
Approximation theory VIII, Vol. 2 (College Station, TX, 1995), pp. 225-234
Ser. Approx. Decompos., Vol. 6, World Sci. Publ., River Edge, NJ, 1995

R. Schneider
Optimal convergence rates of adaptive algorithms for finite element multiscale methods
Boundary value problems and integral equations in nonsmooth domains (Luminy, 1993), pp. 269-284
Lecture Notes in Pure and Applied Mathematics, Vol. 167, Dekker, New York, 1995

W. Dahmen, B. Kleemann, S. Prössdorf, R. Schneider
A multiscale method for the double layer potential equation on a polyhedron
Advances in computational mathematics (New Delhi, 1993), pp. 15-57, Ser. Approx. Decompos., 4, World Sci. Publ., River Edge, NJ, 1994

W. Dahmen, S. Prössdorf, R. Schneider
Multiscale methods for pseudodifferential equations on smooth closed manifolds
Wavelets: theory, algorithms, and applications (Taormina, 1993), pp. 385-424
Wavelet Analysis and its Applications, Vol. 5, Academic Press, San Diego, CA, 1994
DOI: https://doi.org/10.1016/B978-0-08-052084-1.50023-5

W. Dahmen, S. Prössdorf, R. Schneider
Wavelet approximation methods for pseudodifferential equations. I. Stability and convergence
Mathematische Zeitschrift, Vol. 215 (1994), No. 4, pp. 583-620

W. Dahmen, S. Prössdorf, R. Schneider
Multiscale methods for pseudodifferential equations
Recent advances in wavelet analysis, pp. 191 - 235, Wavelet Analysis and its Applications, Vol. 3, Academic Press, Boston, MA, 1994
DOI: https://doi.org/10.1016/B978-0-08-052084-1.50023-5

M. Costabel, F. Penzel, R. Schneider
Convergence of boundary element collocation methods for Dirichlet and Neumann screen problems in R3
Applicable Analysis, Vol. 49 (1993), No. 1-2, pp. 101-117
DOI: https://doi.org/10.1080/00036819308840169

W. Dahmen, S. Prössdorf, R. Schneider
Wavelet approximation methods for pseudodifferential equations - II. Matrix compression and fast solution
Advanced in Computational Mathematics, Vol. 1 (1993), No. 3-4, pp. 259-335
DOI: https://doi.org/10.1007/BF02072014

M. Costabel, F. Penzel, R. Schneider
A collocation method for a screen problem in R3
Symposium "Analysis on Manifolds with Singularities" (Breitenbrunn, 1990), pp. 43-50
Teubner-Texte Math., Vol. 131, Teubner, Stuttgart, 1992
DOI: https://doi.org/10.1007/978-3-663-11577-9_4

Ch. Lubich, R. Schneider
Time discretization of parabolic boundary integral equations
Numerische Mathematik, Vol. 63 (1992), No. 4, pp. 455-481
DOI: https://doi.org/10.1007/BF01385870

S. Prössdorf, R. Schneider
Spline approximation methods for multidimensional periodic pseudodifferential equations
Integral Equations and Operator Theory, Vol. 15 (1992), NO. 4, pp. 626-672
DOI: https://doi.org/10.1007/BF01195782

S. Prössdorf, R. Schneider
Convergence of spline approximation methods for periodic elliptic pseudodifferential equations
Numerical techniques for boundary element methods (Kiel, 1991), pp. 141-152
Notes Numerical Fluid Mechanics, Vol. 33, Vieweg, Braunschweig, 1992
DOI: https://doi.org/10.1007/978-3-663-14005-4_14

M. Costabel, F. Penzel, R. Schneider
Error analysis of a boundary element collocation method for a screen problem in R3
Mathematics of Computation, Vol. 58 (1992), No. 198, pp. 575-586
DOI: https://doi.org/10.2307/2153203

R. Schneider
Reduction of order for pseudodifferential operators on Lipschitz domains
Communications in Partial Differential Equations, Vol. 16 (1991), No. 8-9, pp. 1263-1286
DOI: https://doi.org/10.1080/03605309108820799

R. Schneider
Bessel potential operators for canonical Lipschitz domains
Mathematische Nachrichten, Vol. 150 (1991), pp. 277-299
DOI: https://doi.org/10.1002/mana.19911500120

S. Prössdorf, R. Schneider
A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero
Integral Equations Operator Theory, Vol. 14 (1991), No. 3, pp. 399-435
DOI: https://doi.org/10.1007/BF01218505

R. Schneider
Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations
Numerische Mathematik, Vol. 58 (1991), No. 8, pp. 855-873
DOI: https://doi.org/10.1007/BF01385658

R. Schneider
Nonclassical multidimensional singular integral operators on R+n+1
Integral Equations Operator Theory, Vol. 13 (1990), No. 1, pp. 104-131
DOI: https://doi.org/10.1007/BF01195295

R. Duduchava, R. Schneider
The algebra of nonclassical singular integral operators on half space. Special issue: Wiener-Hopf problems and applications (Oberwolfach 1986)
Integral Equations Operator Theory, Vol. 10 (1987), No. 4, pp. 531-553

R. Schneider
Integral equations with piecewise continuous coefficients in Lp-spaces with weight
Journal of Integral Equations and Applications, Vol. 9 (1985), No. 2, pp. 135-152

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