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H. Rauhut, R. Schneider, Z. Stojanac
Low rank tensor recovery via iterative hard thresholding
Preprint: arxiv: 1602.05217 (2016)
submitted: Applied and Numerical Harmonic Analysis, pp. 419-450

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
(link to journal) (PDF)

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

Numerische Mathematik, (2016), pp. 1-39
(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
(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

94) H. Chen, R. Schneider
Error estimates of some numerical atomic orbitals in molecular simulations
submitted: Communications in Computational Physics, Vol. 18 (2015), No. 1, pp. 125-146

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
(PDF) (PDF, 281,2 KB)

R. Schneider, H. Chen
Numerical analysis of augmented plane wave methods for full-potential electronic structure calculations
ESAIM Math. Model. Numer. Anal. , Vol. 49 (2015), no. 3, pp. 755–785

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
J. Complexity 30 (2014), No. 2, pp. 56-71
(PDF) (PDF, 465,3 KB)

Th. Rohwedder, R. Schneider
Error estimates for the coupled cluster method
ESAIM Math. Model. Numer. Anal. 47 (2013), No. 6, pp. 1553-1582

Ch. Lubich, Th. Rohwedder, R. Schneider, B. Vandereycken
Dynamical approximation by hierarchical Tucker and tensor-train tensors
SIAM J. Matrix Anal. Appl. 34 (2013), No. 2, pp. 470-494

V. Khoromskaia, B. N. Khoromskij, R. Schneider
Tensor-structured factorized calculation of two-electron integrals in a general basis
SIAM J. Sci. Comput. 35 (2013), No. 2, pp. A987-A1010

M. Espig, W. Hackbusch, Th. Rohwedder, R. Schneider
Variational calculus with sums of elementary tensors of fixed rank
Numer. Math. 122 (2012), No. 3, pp. 469-488
(PDF) (PDF, 230,6 KB)

H.-J. Flad, R. Schneider
S*-compressilibity of discrete Hartree-Fock equations
ESAIM Math. Model. Numer. Anal. 46 (2012), No. 5, pp. 1055-1080
(PDF) (PDF, 282,4 KB)

S. Holtz, Th. Rohwedder, R. Schneider
The alternating linear scheme for tensor optimization in the tensor train format
SIAM J. Sci. Comput. 34 (2012), No. 2, pp. A683-A713

H. Harbrecht, M. Peters, R. Schneider
On the low-rank approximation by the pivoted Cholesky decomposition
Appl. Numer. Math. 62 (2012), No. 4, pp. 428-440

S. Holtz, Th. Rohwedder, R. Schneider
On manifolds of tensors of fixed TT-rank
Numer. Math. 120 (2012), No. 4, pp. 701-731

M. Espig, W. Hackbusch, St. Handschuh, R. Schneider
Optimization problems in contracted tensor networks
Comput. Vis. Sci. 14 (2011), No. 6, pp. 271-285

V. Khoromskaia, B. Khoromskij, R. Schneider
QTT representation of the Hartree and exchange operators in electronic structure calculations
Comput. Methods Appl. Math. 11 (2011), no. 3, pp. 327-341

Th. Rohwedder, R. Schneider
An analysis for the DIIS acceleration method used in quantum chemistry calculations
J. Math. Chem. 49 (2011), No. 9, pp. 1889-1914

H.-J. Flad, G. Harutyunyan, R. Schneider, B-W. Schulze
Explicit Green operators for quantum mechanical Hamiltonians. I. The hydrongen atom.
Manuscripta Math. 135 (2011), No. 3-4, pp. 497-519

Th. Rohwedder, R. Schneider, A. Zeiser
Perturbed preconditioned inverse iteration for operator eigenvalue problems with application at adaptive wavelet discretization
Adv. Comput. Math. 34 (2011), No. 1, pp. 43-66
(PDF) (PDF, 1,3 MB)

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
(PDF) (PDF, 370,6 KB)

R. Schneider, O. Reichmann, Ch. Schwab
Wavelet solution of variable order pseudodifferential equations
Calcolo 47 (2010), No. 2, pp. 65-101

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
(PDF) (PDF, 243,0 KB)

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

R. Schneider
Analysis of the projected coupled cluster method in electronic structure calculation (revised version)
Numer. Math. 113 (2009), No. 3, pp. 433-471
(PDF) (PDF, 306,0 KB)

R. Schneider, Th. Rohwedder, J. Blauert
Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
Journal of Comp. Math. (2009), 27, No. 2-3, pp. 360-387
(PDF) (PDF, 362,3 KB)

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
(PDF) (PDF, 913,0 KB)

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

H.-J. Flad, R. Schneider, B. W. Schulze
Asymptotic regularity of solutions to Hartree-Fock equations with Coulomb potential
Math. Methods Appl. Sci. 31 (2008), no. 18, pp. 2172-2201
(PDF) (PDF, 302,9 KB)

W. Dahmen, Th. Rohwedder, R. Schneider, A. Zeiser
Adaptive eigenvalue computation: complexity estimates
Numer. Math. 110 (2008), no. 3, pp. 277–312
(PDF) (PDF, 367,9 KB)

H. Harbrecht, R. Schneider, Ch. Schwab
Multilevel frames for sparse tensor product spaces
Numer. Math. 110 (2008), no. 2, pp. 199–220
(PDF) (PDF, 300,0 KB)

H. Harbrecht, R. Schneider, Ch. Schwab
Sparse second moment analysis for elliptic problems in stochastic domains
Numer. Math. 109 (2008), no. 3, pp. 385–414
(PDF) (PDF, 1,1 MB)

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
J. Chem. Phys. 129, 014109 (2008)
(PDF) (PDF, 542,2 KB)

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
(PDF) (PDF, 1,3 MB)

M. Gnewuch, R. Lindloh, R. Schneider, A. Srivastav
Cubature formulas for function spaces with moderate smoothness
J. Complexity 23 (2007), no. 4-6, pp. 828–850

H.-J. Flad, W. Hackbusch, R. Schneider
Best N-term approximation in electronic structure calculation II. Jastrow factors
M2AN Math. Model. Numer. Anal. 41 (2007), no. 2, pp. 261 –279
(PDF) (PDF, 292,1 KB)

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

K. Eppler, H. Harbrecht, R. Schneider
On convergence in elliptic shape optimization
SIAM J. Control Optim. 46 (2007), no. 1, pp. 61–83
(PDF) (PDF, 296,3 KB)

A. Barinka, W. Dahmen, R. Schneider
Fast computation of adaptive wavelet expansions
Numer. Math. 105 (2007), no. 4, pp. 549–589
(PDF) (PDF, 339,6 KB)

R. Schneider
Adaptive coupled cluster method and CI method for the solution of the electronic Schrödinger equation
Oberwolfach Reports 36 (2007), pp. 2133-2136
(PDF) (PDF, 158,7 KB)

H. Harbrecht, U. Kähler, R. Schneider
Wavelet matrix compression for boundary integral equations. Parallel algorithms and cluster computing
Lect. Notes Comput. Sci. Eng., 52, Springer, Berlin, 2006, pp. 129–149

R. Schneider, T. Weber
Wavelets for density matrix computation in electronic structure calculation
Appl. Numer. Math. 56 (2006), no. 10-11, pp. 1383–1396
(PDF) (PDF, 259,6 KB)

R. Schneider, Y. Xu, A. Zhou
An analysis of discontinuous Galerkin methods for elliptic problems
Adv. Comput. Math. 25 (2006), no. 1-3, pp. 259–286

H.-J. Flad, W. Hackbusch, R. Schneider
Best N term approximation in electronic structure calculations. I. One-electron reduced density matrix
M2AN Math. Model. Numer. Anal. 40 (2006), pp. 49–61
(PDF) (PDF, 384,9 KB)

W. Dahmen, H. Harbrecht, R. Schneider
Compression techniques for boundary integral equations - asymptotically optimal complexity estimates
SIAM J. Numer. Anal. 43, No. 6, pp. 2251-2271 (2006)
(PDF) (PDF, 250,3 KB)

H. Harbrecht, R. Schneider
Wavelet Galerkin schemes for boundary integral equations - implementation and quadrature
SIAM J. Sci. Comput. 27 (2006), No. 4, pp. 1347-1370
(PDF) (PDF, 827,9 KB)

S. Beuchler, R. Schneider, Ch. Schwab
Erratum: Multiresolution weighted norm equivalences and applications
Numer. Math. 98 (2004), No. 1, pp. 67-97
Numer. Math. 102 (2005), No. 2, pp. 365-366

H. Harbrecht, U. Kähler, R. Schneider
Wavelet Galerkin BEM on unstructured meshes
Comput. Visual. Sci. 8 (2005), no. 3-4, pp. 189 –199

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
Comput. Visual. Sci. 8 (2005), no. 3-4, pp. 189 –199

H. Harbrecht, U. Kähler, R. Schneider
Wavelet Matrix Compression for Boundary Integral Equations
GAMM (Proceedings of the GAMM Conference 2005), 5: pp. 767-768 (2005) 

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

H. Harbrecht, R. Schneider
Biorthogonal wavelet bases for the boundary element method
Math. Nachr. 269/270 (2004), pp. 167–188
(PDF) (PDF, 2,0 MB)

S. Beuchler, R. Schneider, Ch. Schwab
Multiresolution weighted norm equivalences and applications
Numer. Math. 98 (2004), no. 1, pp. 67–97

H. Harbrecht, M. Konik, R. Schneider
Fully Discrete Wavelet Galerkin Schemes
Engineering Analysis with Boundary Elements 28, (2004)
(PDF) (PDF, 568,1 KB)

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)

G. N. Gatica, H. Harbrecht, R. Schneider
Least squares methods for the coupling of FEM and BEM
SIAM J. Numer. Anal. 41 (2003), no. 5, pp. 1974–1995

H. Harbrecht, S. Pereverzev, R. Schneider
Self-regularization by projection for noisy pseudodifferential equations of negative order
Numer. Math. 95 (2003), no. 1, pp. 123–143

A. Rathsfeld, R. Schneider
On a quadrature algorithm for the piecewise linear collocation applied to boundary integral equations
Math. Meth. Appl. Sci. 26 (2003), no. 11, pp. 937–979

H. Harbrecht, C. Pérez, F. Paiva, R. Schneider
Multiscale preconditioning for the coupling of FEM-BEM
Numerical Linear Algebra with Applications 10 (2003), no. 3, pp. 197–222

H. Harbrecht, F. Paiva, C. Pérez, R. Schneider
Biorthogonal wavelet approximation for the coupling of FEM-BEM
Numer. Math. 92 (2002), No. 2, pp. 325-356

W. Dahmen, A. Kunoth, R. Schneider
Wavelet least squares methods for boundary value problems
SIAM J. Numer. Anal. 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, Oper. Theory Adv. Appl., 121, Birkhäuser, Basel, 2001

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
Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2001

W. Dahmen, R. Schneider, Y. Xu
Nonlinear functionals of wavelet expansions - adaptive reconstruction and fast evaluation
Numer. Math. 86 (2000), No. 1, pp. 49-101

W. Dahmen, R. Schneider
Wavelets on manifolds. I. Construction and domain decomposition
SIAM J. Math. Anal. 31 (1999), No. 1, pp. 184-230

W. Dahmen, R. Schneider
Composite wavelet bases for operator equations
Math. Comp. 68 (1999), No. 228, pp. 1533-1567

W. Dahmen, R. Schneider
Wavelets with complementary boundary conditions - function spaces on the cube
Results Math. 34 (1998), No. 3-4, pp. 255-293

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

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

T. von Petersdorff, Ch. Schwab, R. Schneider
Multiwavelets for second-kind integral equations
SIAM J. Numer. Anal. 34 (1997), no. 6, pp. 2212-2227

St. Dahlke, W. Dahmen, R. Hochmuth, R. Schneider
Stable multiscale bases and local error estimation for elliptic problems. Multilevel Methods (Oberwolfach, 1995)
Appl. Numer. Math. 23 (1997), No. 1, pp. 21-47

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 Numer. Fluid mech., 54, Vieweg, Braunschweig, 1996

W. Dahmen, B. H. Kleemann, S. Prössdorf, R. Schneider
Multiscale methods for pseudodifferential equations
ICIAM/GAMM 95 (Hamburg, 1995)
Z. Angew. Math. Mech. 76 (1996), suppl. 1, pp. 7-10

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 Appl. Math., 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., 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 Appl. Math., 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 Anal. Appl. 5, Academic Press, San Diego, CA, 1994

W. Dahmen, S. Prössdorf, R. Schneider
Wavelet approximation methods for pseudodifferential equations. I. Stability and convergence
Math. Z. 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 Anal. Appl., 3, Academic Press, Boston, MA, 1994

M. Costabel, F. Penzel, R. Schneider
Convergence of boundary element collocation methods for Dirichlet and Neumann screen problems in R3
Appl. Anal. 49 (1993), No. 1-2, pp. 101-117

W. Dahmen, S. Prössdorf, R. Schneider
Wavelet approximation methods for pseudodifferential equations - II. Matrix compression and fast solution
Adv. Comput. Math. 1 (1993), No. 3-4, pp. 259-335

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., 131, Teubner, Stuttgart, 1992

Ch. Lubich, R. Schneider
Time discretization of parabolic boundary integral equations
Numer. Math. 63 (1992), No. 4, pp. 455-481

S. Prössdorf, R. Schneider
Spline approximation methods for multidimensional periodic pseudodifferential equations
Integral Equations Operator Theory, 15 (1992), NO. 4, pp. 626-672

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 Numer. Fluid Mech., 33, Vieweg, Braunschweig, 1992

M. Costabel, F. Penzel, R. Schneider
Error analysis of a boundary element collocation method for a screen problem in R3
Math. Comp. 58 (1992), No. 198, pp. 575-586

R. Schneider
Reduction of order for pseudodifferential operators on Lipschitz domains
Comm. Partial Differential Equations 16 (1991), No. 8-9, pp. 1263-1286

R. Schneider
Bessel potential operators for canonical Lipschitz domains
Math. Nachr. 150 (1991), pp. 277-299

S. Prössdorf, R. Schneider
A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero
Integral Equations Operator Theory, 14 (1991), No. 3, pp. 399-435

R. Schneider
Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations
Numer. Math. 58 (1991), No. 8, pp. 855-873 

R. Schneider
Nonclassical multidimensional singular integral operators on R+n+1
Integral Equations Operator Theory 13 (1990), No. 1, pp. 104-131

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, 10 (1987), No. 4, pp. 531-553

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

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