Lehrstuhl für Wissenschaftliches Rechnen

Publikationen

Publikationen pro Jahr 1999 2006 2007 2016 2024 2024

• 29 Artikel
• 2 Kapitel
• 1 Vorwort/Nachwort

Publikationen pro Jahr

Publikationen pro Jahr

Suchergebnisse

• 2024

  A Stirling-Type Formula for the Distribution of the Length of Longest Increasing Subsequences

  Bornemann, F., Juni 2024, in: Foundations of Computational Mathematics. 24, 3, S. 915-953 39 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Random Matrices 100%
  • Stirling-type 100%
  • Longest Increasing Subsequence 100%
  • Asymptotics 100%
  • Random Matrix 100%
  4 Zitate (Scopus)

• Asymptotic expansions relating to the distribution of the length of longest increasing subsequences

  Bornemann, F., 15 März 2024, in: Forum of Mathematics, Sigma. 12, e36.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Length Distribution 100%
  • Asymptotic Expansion 100%
  • Longest Increasing Subsequence 100%
  • Subsequence 100%
  • Depoissonization 66%
  2 Zitate (Scopus)

• Asymptotic Expansions Relating to the Lengths of Longest Monotone Subsequences of Involutions

  Bornemann, F., 2024, (Angenommen/Im Druck) in: Experimental Mathematics.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Asymptotic Expansion 100%
  • Involution 100%
  • Monotone Subsequence 100%
  • Fixed-point-free 100%
  • Fixed Points 100%
• 2023

  A Jentzsch-Theorem for Kapteyn, Neumann and General Dirichlet Series

  Bornemann, F., Dez. 2023, in: Computational Methods and Function Theory. 23, 4, S. 723-739 17 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Jentzsch's Theorem 100%
  • General Dirichlet Series 100%
  • Dirichlet Series 100%
  • Growth Function 66%
  • Power Series 66%
  1 Zitat (Scopus)
• 2022

  The challenge of sixfold integrals: the closed-form evaluation of Newton potentials between two cubes

  Bornemann, F., 29 Juni 2022, in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478, 2262, 20220254.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Newtonian Potential 100%
  • Closed-form Evaluation 100%
  • Closed Form 100%
  • Cube 100%
  • Form Evaluation 100%
• 2021

  Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical Chains

  Mendl, C. B. & Bornemann, F., März 2021, in: Journal of Statistical Physics. 182, 3, 57.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Numerical Evaluation 100%
  • Classical Systems 100%
  • Semiclassical 100%
  • Thermodynamic Quantities 100%
  • Discretization 100%
• 2020

  Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid

  Bornemann, F., Li, Y. Y. & Wuttke, J., 1 Mai 2020, in: Acta Crystallographica Section A: Foundations and Advances. 76, S. 376-389 14 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Transport Equation 100%
  • Mosaic Crystals 100%
  • Darwin-Hamilton Equations 100%
  • Multiple Bragg Reflection 100%
  • Bragg Reflection 100%
  2 Zitate (Scopus)
• 2017

  Finite Size Effects for Spacing Distributions in Random Matrix Theory: Circular Ensembles and Riemann Zeros

  Bornemann, F., Forrester, P. J. & Mays, A., Mai 2017, in: Studies in Applied Mathematics. 138, 4, S. 401-437 37 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Random Matrix Theory 100%
  • Leading Terms 100%
  • Space Distribution 100%
  • Riemann Zeros 100%
  • Circular Ensembles 100%
  19 Zitate (Scopus)
• 2016

  A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge

  Bornemann, F., Juni 2016, in: Annals of Applied Probability. 26, 3, S. 1942-1946 5 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Correction Term 100%
  • Laguerre Unitary Ensemble 100%
  • Hard Edge 100%
  • Smallest Eigenvalue Distribution 100%
  • Edge 100%
  11 Zitate (Scopus)

• Numerical methods for the discrete map Z^a

  Bornemann, F., Its, A., Olver, S. & Wechslberger, G., 1 Jan. 2016, Advances in Discrete Differential Geometry. Springer Berlin Heidelberg, S. 151-176 26 S.

  Publikation: Beitrag in Buch/Bericht/Konferenzband › Kapitel › Begutachtung

  Open Access

  • Numerical Methods 100%
  • Discrete Map 100%
  • Mathematical Method 100%
  • Numerical Examples 50%
  • Accurate Evaluation 50%

• On the scaling limits of determinantal point processes with kernels induced by sturm-liouville operators

  Bornemann, F., 19 Aug. 2016, in: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 12, 083.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Scaling Limit 100%
  • Determinantal Point Processes 100%
  • Sturm-Liouville Operator 100%
  • Point Process 100%
  • Edge 50%
  8 Zitate (Scopus)

• Singular values and evenness symmetry in random matrix theory

  Bornemann, F. & Forrester, P. J., 1 Sept. 2016, in: Forum Mathematicum. 28, 5, S. 873-891 19 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Random Matrix Theory 100%
  • Singular Values 100%
  • Singular Value 100%
  • Unitary Symmetry 60%
  • Gauss 40%
  5 Zitate (Scopus)

• The SIAM 100-Digit Challenge: A Decade Later: Inspirations, Ramifications, and Other Eddies Left in Its Wake

  Bornemann, F., Juni 2016, in: Jahresbericht der Deutschen Mathematiker-Vereinigung. 118, 2, S. 87-123 37 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  • Eddies 100%
  • 100-digit Challenge 100%
  • Manifold 100%
  • Mathematics 100%
  • Summation 100%
  3 Zitate (Scopus)
• 2015

  The singular values of the GOE

  Bornemann, F. & La Croix, M., 1 Apr. 2015, in: Random Matrices: Theory and Application. 4, 2, 1550009.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  • Singular Values 100%
  • Gaussian Orthogonal Ensemble 100%
  • Gaussian Distribution 100%
  • Singular Value 100%
  • Gap Probability 40%
  6 Zitate (Scopus)
• 2014

  Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlevé II Transcendents

  Wechslberger, G. & Bornemann, F., Feb. 2014, in: Constructive Approximation. 39, 1, S. 151-171 21 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Riemann-Hilbert Problem 100%
  • Numerical Methods 33%
  • Mathematical Method 33%
  • Optimization Problem 16%
  • Shortest Path 16%
  4 Zitate (Scopus)
• 2013

  Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles

  Witte, N. S., Bornemann, F. & Forrester, P. J., Juni 2013, in: Nonlinearity. 26, 6, S. 1799-1822 24 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Joint Distribution 100%
  • Second Eigenvalue 100%
  • Unitary Ensembles 100%
  • First Eigenvalue 100%
  • Soft Edge 100%
  19 Zitate (Scopus)

• Optimal contours for high-order derivatives

  Bornemann, F. & Wechslberger, G., Apr. 2013, in: IMA Journal of Numerical Analysis. 33, 2, S. 403-412 10 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Minimizes 100%
  • Step Size 100%
  • Analytic Function 100%
  • Holomorphic Function 100%
  • Integration Problem 100%
  7 Zitate (Scopus)
• 2012

  On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity

  Xiang, S. & Bornemann, F., 2012, in: SIAM Journal on Numerical Analysis. 50, 5, S. 2581-2587 7 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Convergence Rate 100%
  • Quadrature Rules 100%
  • Gauss 100%
  • Clenshaw-Curtis Quadrature 100%
  • Polynomial 100%
  36 Zitate (Scopus)
• 2011

  Accuracy and Stability of Computing High-order Derivatives of Analytic Functions by Cauchy Integrals

  Bornemann, F., Feb. 2011, in: Foundations of Computational Mathematics. 11, 1, S. 1-63 63 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Higher-order Derivatives 100%
  • Analytic Functions 100%
  • Cauchy Integral 100%
  • Analytic Function 100%
  • Integral 100%
  46 Zitate (Scopus)
• 2010

  Asymptotic independence of the extreme eigenvalues of Gaussian unitary ensemble

  Bornemann, F., Feb. 2010, in: Journal of Mathematical Physics. 51, 2, 023002JMP.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Asymptotic Independence 100%
  • Gaussian Unitary Ensemble 100%
  • Extreme Eigenvalues 100%
  • Asymptotics 100%
  • Gaussian Distribution 100%
  15 Zitate (Scopus)

• On the numerical evaluation of fredholm determinants

  Bornemann, F., Apr. 2010, in: Mathematics of Computation. 79, 270, S. 871-915 45 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Numerical Evaluation 100%
  • Fredholm Determinant 100%
  • Fredholm 100%
  • Random Matrix Theory 50%
  • Integral Operator 50%
  211 Zitate (Scopus)
• 2008

  The airy₁ process is not the limit of the largest eigenvalue in GOE matrix diffusion

  Bornemann, F., Ferrari, P. L. & Prähofer, M., Nov. 2008, in: Journal of Statistical Physics. 133, 3, S. 405-415 11 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  • Largest Eigenvalue 100%
  • Limit Laws 100%
  • Matrix Diffusion 100%
  • Diffusion Matrix 100%
  • Fredholm Determinant 50%
  30 Zitate (Scopus)

• The chebop system for automatic solution of differential equations

  Driscoll, T. A., Bornemann, F. & Trefethen, L. N., Dez. 2008, in: BIT Numerical Mathematics. 48, 4, S. 701-723 23 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Automatic Solution 100%
  • Solution of Differential Equations 100%
  • Matrix Laboratory (MATLAB) 100%
  • Chebop 100%
  • Space Dimension 100%
  63 Zitate (Scopus)
• 2007

  A model for understanding numerical stability

  Bornemann, F., Apr. 2007, in: IMA Journal of Numerical Analysis. 27, 2, S. 219-231 13 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Numerical Stability 100%
  • Rounding Error Analysis 100%
  • Roundoff Error 100%
  • Error Analysis 100%
  • Iterative Refinement 50%
  3 Zitate (Scopus)

• Fast image inpainting based on coherence transport

  Bornemann, F. & März, T., Juli 2007, in: Journal of Mathematical Imaging and Vision. 28, 3, S. 259-278 20 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  • Image Inpainting 100%
  • Coherence Transport 100%
  • Tensor 100%
  • Partial Differential Equation 100%
  • Transport Equation 100%
  183 Zitate (Scopus)

• Taming a hydra of singularities

  Bornemann, F. & Schmelzer, T., Okt. 2007, in: American Mathematical Monthly. 114, 8, S. 727-732 6 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access
• 2006

  Energy level crossings in molecular dynamics

  Bornemann, F., Lasser, C. & Swart, T., 2006, Analysis, Modeling and Simulation of Multiscale Problems. Springer Berlin Heidelberg, S. 577-594 18 S.

  Publikation: Beitrag in Buch/Bericht/Konferenzband › Kapitel › Begutachtung

  • Molecular Dynamics 100%
  • Energy-level Crossing 100%
  • electronics 100%
  • Molecular Systems 50%
  • Electronic Level 50%

• Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle

  Bornemann, F. & Rasch, C., Juli 2006, in: Computing and Visualization in Science. 9, 2, S. 57-69 13 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Equation-based 100%
  • Finite Element Discretization 100%
  • Local Variational Principle 100%
  • Static Hamilton-Jacobi Equations 100%
  • Dirichlet Problem 100%
  71 Zitate (Scopus)

• Preface

  Bornemann, F., Luckhaus, S., Mielke, A. & Müller, S., 2006, Analysis, Modeling and Simulation of Multiscale Problems. Springer Berlin Heidelberg, S. V-VII

  Publikation: Beitrag in Buch/Bericht/Konferenzband › Vorwort/Nachwort

  Open Access
• 2003

  Sparsing in real time simulation

  Schiela, A. & Bornemann, F., 2003, in: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 83, 10, S. 637-647 11 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  Open Access

  • Time-dependent Simulation 100%
  • Simulation Time 100%
  • Real-Time Simulation 100%
  • Jacobian 66%
  • Explicit Method 66%
  11 Zitate (Scopus)
• 1999

  Adaptive accuracy control for Car-Parrinello simulations

  Bornemann, F. A. & Schütte, C., Aug. 1999, in: Numerische Mathematik. 83, 2, S. 179-186 8 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  • Control Accuracy 100%
  • Adaptive Accuracy 100%
  • Car-Parrinello 100%
  • Approximation (Algorithm) 100%
  • Typical Example 100%
  5 Zitate (Scopus)

• On the singular limit of the quantum-classical molecular dynamics model

  Bornemann, F. A. & Schütte, C., 1999, in: SIAM Journal on Applied Mathematics. 59, 4, S. 1208-1224 17 S.

  Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

  • Quantum Approach 100%
  • Classical Molecular Dynamics 100%
  • Molecular Dynamics Model 100%
  • Singular Limit 100%
  • Dynamic Models 100%
  17 Zitate (Scopus)