BannerHauptseite TUMHauptseite LehrstuhlMathematik SchriftzugHauptseite LehrstuhlHauptseite Fakultät

Google Scholar PfeilScopus PfeilErdős number Pfeil

Publications of Folkmar Bornemann

MathSciNet PfeilZentralblattarXiv Pfeil


  1. Numerische lineare Algebra Pfeil, 2. Auflage, Springer-Verlag, Berlin, Heidelberg (2018). (1. Auflage 2016)
  2. Funktionentheorie Pfeil, 2. Auflage, Birkhäuser, Basel (2016). Errata (1. Auflage 2013; Zbl 1262.30001 Pfeil.)
  3. Konkrete Analysis Pfeil, Springer-Verlag, Berlin, Heidelberg, New York (2008). Zbl. 1158.00004 Pfeil. Errata
  4. (with D. Laurie, S. Wagon, J. Waldvogel) The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing Pfeil, Society of Industrial Applied Mathematics (SIAM), Philadelphia (2004). MR 2005c:65002 Pfeil; Zbl. 1060.65002 Pfeil.
  5. Homogenization in Time of Singularly Perturbed Mechanical Systems. Lecture Notes in Mathematics 1687 Pfeil, Springer-Verlag, Berlin, Heidelberg, New York (1998). MR 99g:34105; Zbl. 902.34051.
  6. (with P. Deuflhard) Numerische Mathematik II. Gewöhnlicher Differentialgleichungen Pfeil. 4. durchgesehene und ergänzte Auflage. Verlag Walter de Gruyter, Berlin, New York (2013). (3. Auflage 2008; 2. Auflage 2002; Zbl. 1004.65074. 1. Auflage 1994; MR 97e:65001; Zbl. 856.65080.)


  1. Asymptotic expansions relating to the distribution of the length of longest increasing subsequences Pfeil, arXiv:2301.02022 Pfeil, 42pp (2023).
  2. A Stirling-type formula for the distribution of the length of longest increasing subsequences Pfeil, Found. Comput. Math. Pfeil 39pp (online first, 2023). DOI 10.1007/s10208-023-09604-z Pfeil
  3. The Challenge of Sixfold Integrals: The Closed-Form Evaluation of Newton Potentials between Two Cubes, Proc. R. Soc. A 478:20220254 Pfeil, 20pp (2022). DOI 10.1098/rspa.2022.0254 Pfeil
  4. A Jentzsch-Theorem for Kapteyn, Neumann, and General Dirichlet Series Pfeil, Comput. Methods Func. Theory Pfeil 17pp (online first, 2022). DOI 10.1007/s40315-022-00468-y Pfeil
  5. (with C.B. Mendl) Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains, J. Stat. Phys. 182:57 Pfeil, 14pp (2021). DOI 10.1007/s10955-021-02736-y Pfeil
  6. (with Y.Y. Li and J. Wuttke) Multiple Bragg reflection by a thick mosaic crystal. II. Simplified transport equation solved on a grid, Acta Cryst. A76 Pfeil, 376–389 (2020). DOI 10.1107/S2053273320002065 Pfeil
  7. (with P.J. Forrester and A. Mays) Finite size effects for spacing distributions in random matrix theory: circular ensembles and Riemann zeros, Stud. Appl. Math. 138 Pfeil, 401-437 (2017). DOI 10.1111/sapm.12160 Pfeil; (selected for Highlights of the Year 2017) Pfeil
  8. On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators Pfeil, SIGMA Symmetry Integrability Geom. Methods Appl. 12 Pfeil, 083, 20pp (2016). DOI 10.3842/SIGMA.2016.083 Pfeil
  9. The SIAM 100-Digit Challenge: A Decade Later, Jahresber. Dtsch. Math.-Ver. 118 Pfeil, pp. 87-123 (2016). DOI 10.1365/s13291-016-0137-2 Pfeil. Errata
  10. Computing Random Matrix Distributions and Operator Determinants, to appear in: R. Benguria, A. Ramirez, E. Stockmeyer (Eds.), Proceedings of the Proceedings of the XVIIIth International Congress on Mathematical Physics (Santiago de Chile 2015), World Scientific; 18pp., (2016).
  11. (with A. Its, S. Olver, G. Wechslberger) Numerical Methods for the Discrete Map \(Z^a\) Pfeil, in: A. Bobenko (Ed.), Advances in Discrete Differential Geometry Pfeil, Springer-Verlag, pp. 151-176 (2016). DOI 10.1007/978-3-662-50447-5_4 Pfeil
  12. A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge, Ann. Appl. Probab. 26 Pfeil, pp. 1942-1946 (2016). DOI 10.1214/15-AAP1121 Pfeil
  13. (with P.J. Forrester) Singular values and evenness symmetry in random matrix theory, Forum Math. 28 Pfeil; pp. 873-891 (2016). DOI 10.1515/forum-2015-0055 Pfeil
  14. (with M. La Croix) The singular values of the GOE, Random Matrices Theory Appl. 4 Pfeil, 1550009, 32pp (2015). DOI 10.1142/S2010326315500094 Pfeil
  15. (with G. Wechslberger) Automatic deformation of Riemann-Hilbert problems with applications to the Painlevé II transcendents, Constr. Approx. 39 Pfeil, pp. 151-171 (2014). DOI 10.1007/s00365-013-9199-x Pfeil
  16. (with N.S. Witte and P.J.Forrester) Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles, Nonlinearity 26 Pfeil, pp. 1799-1822 (2013). DOI 10.1088/0951-7715/26/6/1799 Pfeil.
  17. (with G. Wechslberger) Optimal Contours for High-Order Derivatives, IMA J. Numer. Anal. 33 Pfeil, pp. 403-412 (2013). DOI 10.1093/imanum/drs030 Pfeil.
  18. (with S. Xiang) On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity, SIAM J. Numer. Anal. 50 Pfeil, pp. 2581-2587 (2012). DOI 10.1137/120869845 Pfeil. Zbl. 1259.65059.
  19. Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals. Found. Comput. Math. 11 Pfeil, pp. 1-63 (2011). DOI 10.1007/s10208-010-9075-z Pfeil. MR 2012a:65061; Zbl. 1213.65039.
  20. On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review. Markov Processes Relat. Fields 16 Pfeil, pp. 803-866 (2010). MR2895091, Zbl. 1222.60013.
  21. Asymptotic Independence of the Extreme Eigenvalues of GUE. J. Math. Phys. 51 Pfeil, 023514, 8pp. (2010). DOI 10.1063/1.3290968 Pfeil. MR 2011b:82038.
  22. On the Numerical Evaluation of Fredholm Determinants. Math. Comp. 79 Pfeil, pp. 871-915 (2010). DOI 10.1090/s0025-5718-09-02280-7 Pfeil. MR 2011b:65069; Zbl. 1208.65182. Erratum
  23. (with T. A. Driscoll and L. N. Trefethen) The Chebop System for Automatic Solution of Differential Equations. BIT 48 Pfeil, pp. 701-723 (2008). DOI 10.1007/s10543-008-0198-4 Pfeil. MR 2009j:65381; Zbl. 1162.65370.
  24. (with P. L. Ferrari and M. Prähofer) The Airy1 process is not the limit of the largest eigenvalue in GOE matrix diffusion. J. Stat. Phys. 133 Pfeil, pp. 405-415 (2008). DOI 10.1007/s10955-008-9621-0 Pfeil. MR 2009j:60214; Zbl. 1161.82340.
  25. (with T. März) Fast Image Inpainting Based on Coherence Transport. J. Math. Imaging Vis. 28 Pfeil, pp. 259-278 (2007). DOI 10.1007/s10851-007-0017-6 Pfeil. Because the publisher has corrupted the image quality: version with high quality images. MR 2367298.
  26. (with T. Schmelzer) Taming a Hydra of Singularities. Amer. Math. Monthly 114 Pfeil, pp. 727-732 (2007). MR 2354442; Zbl 1154.26012.
  27. A Model for Understanding Numerical Stability. IMA J. Numer. Anal. 27 Pfeil, pp. 219-231 (2007). DOI 10.1093/imanum/drl037 Pfeil. MR 2008c:65122; Zbl. 1114.65041.
  28. (with C. Lasser and T. Swart) Energy level crossings in molecular dynamics. In: A. Mielke (Ed.), "Analysis, Modeling, and Simulation of Multiscale Problems", pp. 577-594, Springer-Verlag (2006). MR 2007k:81229.
  29. (with C. Rasch) Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle. Comput. Visual Sci. 9 Pfeil, pp. 57-69 (2006). DOI 10.1007/s00791-006-0016-y Pfeil. MR 2007c:65102.
  30. (with D. Laurie, S. Wagon, J. Waldvogel) Challenges in Numerical Computation. In: T. E. Simos et al. (Eds.), Proc. ICNAAM 2004, pp. 232-234, Wiley-VCH (2004). Zbl 1060.65570.
  31. (with A. Schiela) Sparsing in Real Time Simulation. Z. angew. Math. Mech. 83 Pfeil, pp. 637-647 (2003). MR 2004j:65107; Zbl. 1032.65089.
  32. Normen zur Charakterisierung der schwach*-Konvergenz beschränkter Folgen. Math. Semesterber. 48 Pfeil, pp. 247-260 (2002). MR 2003h:46030; Zbl. 1032.46010.
  33. Runge-Kutta Methods, Trees, and Maple. Selçuk J. Appl. Math. 2, pp. 3-15 (2001). Zbl. 1011.65051. Version using Mathematica: E-print arXiv:math.NA/0211049 Pfeil.
  34. (with C. Schütte) Adaptive Accuracy Control of Car-Parrinello Simulations. Numer. Math. 83 Pfeil, pp. 179-186 (1999). MR 2000e:65122; Zbl. 933.81005.
  35. (with C. Schütte) On the Singular Limit of the Quantum-Classical Molecular Dynamics Model. SIAM J. Appl. Math. 59 Pfeil, pp. 1208-1224 (1999). MR 2000c:81067; Zbl. 926.34073.
  36. (with C. Schütte) Approximation Properties and Limits of the Quantum-Classical Molecular Dynamics Model. In: P. Deuflhard, J. Hermans et al. (Eds.), ``Computational Molecular Dynamics: Challenges, Methods, Ideas'', pp. 380-395, Springer-Verlag (1999). MR 2000g:81003; Zbl. 966.81063.
  37. (with M. Schemann) An Adaptive Rothe Method for the Wave Equation. Comput. Visual Sci. 1 Pfeil, pp. 137-144 (1998). Zbl. 915.65105.
  38. (with R. Krause) Classical and Cascadic Multigrid - A Methodological Comparison. In: P. Bjorstad, M. Espedal, D. Keyes (Eds.), ``Proc. 9th Int'l. Conference on Domain Decomposition Methods 1996, Ullensvang, Norway'', pp. 64-71, Domain Decomposition Press, Bergen 1998.
  39. (with C. Schütte) A Mathematical Investigation of the Car-Parrinello Method. Numer. Math. 78 Pfeil, pp. 359-376 (1998). MR 99d:81183; Zbl. 887.34026.
  40. (with C. Schütte) Homogenization Approach to Smoothed Molecular Dynamics. Nonlinear Analysis 30 Pfeil, pp. 1805-1814 (1997). MR 99b:70016; Zbl. 920.70018.
  41. (with C. Schütte) Homogenization of Hamiltonian Systems with a Strong Constraining Potential. Physica D 102, pp. 57-77 (1997). MR 99a:70025; Zbl. 896.70010.
  42. (with P. Deuflhard) Cascadic Multigrid Methods. In: R. Glowinski, J. Périaux, Z. Shi, O. Widlund (Eds.), ``Domain Decomposition Methods in Sciences and Engineering'', pp. 205-212, John Wiley & Sons, Chichester, New York (1997).
  43. (with P. Nettesheim, B. Schmidt, C. Schütte) An Explicit and Symplectic Integrator for Quantum-Molecular Dynamics. Chem. Phys. Lett. 256, pp. 581-588 (1996).
  44. (with P. Nettesheim, C. Schütte) Quantum-classical Molecular Dynamics as an Approximation to Full Quantum Dynamics. J. Chem. Phys. 105, pp. 1074-1083 (1996).
  45. (with P. Deuflhard) The Cascadic Multigrid Method for Elliptic Problems. Numer. Math. 75 Pfeil, pp. 135-152 (1996). MR 98a:65175; Zbl. 873.65107.
  46. (with B. Erdmann, R. Kornhuber) A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions. SIAM J. Numer. Anal. 33, pp. 1188-1204 (1996). MR 98a:65161; Zbl. 863.65069.
  47. Interpolation Spaces and Optimal Multilevel Preconditioners. In: D. Keyes, J. Xu (Eds.), ``Proceedings of the 7th International Conference on Domain Decomposition Methods 1993'', pp. 3-8. AMS, Providence (1994). MR 95j:65155; Zbl. 818.65107.
  48. Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. In: W. Hackbusch, G. Wittum (Eds.),``Adaptive Methods - Algorithms, Theory and Applications'', pp. 69-83, Vieweg Verlag, Braunschweig, Wiesbaden (1994). Zbl. 810.65088.
  49. (with H. Yserentant) A Basic Norm Equivalence for the Theory of Multilevel Methods. Numer. Math. 64, pp. 455-476 (1993). MR 94b:65155; Zbl. 796.65135.
  50. (with B. Erdmann, R. Kornhuber) Adaptive Multilevel Methods in Three Space Dimensions. Inter. J. Numer. Meth. Engrg. 36, pp. 3187-3202 (1993). MR 94d:65057; Zbl. 780.73073.
  51. Adaptive Multilevel Solution of Parabolic Equations in 3D. In: R. Vichnevetsky, D. Knight, G. Richter (Eds.), ``Proceedings of the 7th IMACS International Conference on Computer Methods for Partial Differential Equations'', New Brunswick, New Jersey, 1992, pp. 75-81. IMACS Secretariat, New Brunswick (1992).
  52. An Adaptive Multilevel Approach to Parabolic Equations III. 2D Error Estimation and Multilevel Preconditioning. IMPACT Comput. Sci. Engrg. 4, pp. 1-45 (1992). MR 93g:65126; Zbl. 745.65055.
  53. An Adaptive Multilevel Approach to Parabolic Equations II. Variable Order Time Discretization Based on a Multiplicative Error Correction. IMPACT Comput. Sci. Engrg. 3, pp. 93-122 (1991). MR 92k:65140; Zbl. 735.65066.
  54. An Adaptive Multilevel Approach to Parabolic Equations I. General Theory and 1D-Implementation. IMPACT Comput. Sci. Engrg. 2, pp. 279-317 (1990). Zbl. 722.65055.

Book reviews

  1. Modern Aspects of Random Matrix Theory (V. Vu ed.), SIAM Rev. 57, pp. 632-634 (2015).
  2. The Computer as Crucible: An Introduction to Experimental Mathematics (J. Borwein, K. Devlin), Math. Semesterber. 57, pp. 139–142 (2010).

Papers for a general audience

  1. (with S. Wagon) A perplexing polynomial puzzle, revisited. College Math. J. 36, p. 288 (2005).
  2. (with G. Ziegler) Die Beweise des Sommers. Mitteilungen der DMV 12, pp. 181-183 (2004).
  3. PRIMES Is in P: A Breakthrough for "Everyman" Pfeil. Notices of the AMS 50, pp. 545-552 (2003). Translation by Harold P. Boas. MR 2004c:11237; Zbl. 1067.11080.
    • Reprinted in Mathematics Newsletter of the Ramanujan Mathematical Society 13, No. 1&2, pp. 1-10 (2003).
    • German original: PRIMES is in P: Ein Durchbruch für "Jedermann". Mitteilungen der DMV 4-2002, pp. 14-21 (2002). MR 2003m:68004.
    • Abridged German version: PRIMES is in P: Ein Durchbruch für "Jedermann". Computeralgebra-Rundbrief 32, pp. 6-14 (2003).
    • Reprint of German original in: E. Behrends, P. Gritzmann, G. M. Ziegler (Eds.), Pi und Co., Kaleidoskop der Mathematik Pfeil, pp. 55-62 (2008).
    • French translation: PRIMES is in P, une avancée accessible à «l'homme ordinaire». Gazette des Mathématiciens 98 Pfeil, pp. 14-29 (2003). Translation by Colette Anné. Zbl. 1067.11079.

Unpublished Notes & Papers

  1. On Hathaway's circular pursuit problem, (April 2011).
  2. On Bellman's linear search problem, (March 2010).
  3. (with W. Boiger) Local Morphological Schemes for the Affine Morphological Scale Space. Preprint, 17pp, Technische Universität München (March 2006).
  4. An Experimental Approach to the Singular Modulus k100, (March 2005).
  5. How Mathematica and Maple Get Meijer's G-function into Definite Integrals, (February 2005).
  6. Solution of a Problem Posed by Jörg Waldvogel, (July 2003).
  7. Short Remarks on the Solution of the SIAM 100-digit Challenge, (May 2002).
  8. Zur Eindeutigkeit der Viskositätslösungen beim Cauchy-Problem von Hamilton-Jacobi Gleichungen, (October 2000).
  9. Homogenization in Time II: Mechanical Systems Subject to Friction and Gyroscopic Forces. SC-97-65 Pfeil, Konrad-Zuse-Zentrum Berlin (1997).
  10. A Note on the Adiabatic Theorem of Quantum Mechanics, (August 1997).
  11. On Microlocal Obstructions to the Compactness of Sequences, (September 1996).
  12. (with C. Schütte) A Mathematical Approach to Smoothed Molecular Dynamics: Correcting Potentials for Freezing Bond Angles. SC 95-30 Pfeil, Konrad-Zuse-Zentrum Berlin (1995).
  13. On the Convergence of Cascadic Iterations for Elliptic Problems. SC 94-08 Pfeil, Konrad-Zuse-Zentrum Berlin (1994).
  14. Die Maximalwinkelbedingung für Finite Elemente, (December 1993).
  15. A Sharpened Condition Number Estimate for the BPX Preconditioner of Elliptic Finite Element Problems on Highly Nonuniform Triangulations. SC 91-09 Pfeil, Konrad-Zuse-Zentrum Berlin (1991).
  16. (with B. Erdmann, R. Roitzsch) KASKADE: Numerical Experiments. TR 91-01 Pfeil, Konrad-Zuse-Zentrum Berlin (1991).

Unpublished Lecture Notes

  1. Quantenrechnen (Quantum Computation) Pfeil, Technische Universität München (2003).


  1. Homogenization in Time of Singularly Perturbed Conservative Mechanical Systems. Habilitationsschrift, Freie Universität Berlin, VI+150pp; revised and enlarged version published as the Springer Lecture Notes in Mathematics #1687.
  2. An Adaptive Multilevel Approach for Parabolic Equations in Two Space Dimensions. Dissertation, Freie Universität Berlin, 136pp; published as TR 91-07 Pfeil, Konrad-Zuse-Zentrum Berlin (1991).
  3. Adaptive Multilevel Discretization in Time and Space for Parabolic Partial Differential Equations. Diplomarbeit, Freie Universität Berlin, 75pp; published as TR 89-07 Pfeil, Konrad-Zuse-Zentrum Berlin (1989).

Pauca sed Matura.   Johann Carl Friedrich Gauß