


Publications of Folkmar Bornemann


Books
- Numerische lineare Algebra
, 2. Auflage, Springer-Verlag, Berlin, Heidelberg (2018). (1. Auflage 2016)
- English translation: Numerical Linear Algebra
, Springer-Verlag, Cham (2018).
- English translation: Numerical Linear Algebra
- Funktionentheorie
, 2. Auflage, Birkhäuser, Basel (2016). Errata (1. Auflage 2013; Zbl 1262.30001
.)
- Konkrete Analysis
, Springer-Verlag, Berlin, Heidelberg, New York (2008). Zbl. 1158.00004
. Errata
- (with D. Laurie, S. Wagon, J. Waldvogel) The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing
, Society of Industrial Applied Mathematics (SIAM), Philadelphia (2004). MR 2005c:65002
; Zbl. 1060.65002
.
- German translation: Vom Lösen numerischer Probleme
, Springer-Verlag, Berlin, Heidelberg, New York (2006). Zbl. 1158.65001
.
- German translation: Vom Lösen numerischer Probleme
- Homogenization in Time of Singularly Perturbed Mechanical Systems. Lecture Notes in Mathematics 1687
, Springer-Verlag, Berlin, Heidelberg, New York (1998). MR 99g:34105; Zbl. 902.34051.
- (with P. Deuflhard) Numerische Mathematik II. Gewöhnlicher Differentialgleichungen
. 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.)
- English translation: Scientific Computing with Ordinary Differential Equations
. Springer-Verlag, New York, Heidelberg, Berlin (2002). MR 2003e:65001; Zbl. 1001.65071.
- English translation: Scientific Computing with Ordinary Differential Equations
Papers
- Asymptotic expansions relating to the distribution of the length of longest increasing subsequences
, arXiv:2301.02022
, 42pp (2023).
- A Stirling-type formula for the distribution of the length of longest increasing subsequences
, Found. Comput. Math.
39pp (online first, 2023). DOI 10.1007/s10208-023-09604-z
- The Challenge of Sixfold Integrals: The Closed-Form Evaluation of Newton Potentials between Two Cubes, Proc. R. Soc. A 478:20220254
, 20pp (2022). DOI 10.1098/rspa.2022.0254
- A Jentzsch-Theorem for Kapteyn, Neumann, and General Dirichlet Series
, Comput. Methods Func. Theory
17pp (online first, 2022). DOI 10.1007/s40315-022-00468-y
- (with C.B. Mendl) Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains, J. Stat. Phys. 182:57
, 14pp (2021). DOI 10.1007/s10955-021-02736-y
- (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
, 376–389 (2020). DOI 10.1107/S2053273320002065
- (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
, 401-437 (2017). DOI 10.1111/sapm.12160
; (selected for Highlights of the Year 2017)
- On the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm-Liouville Operators
, SIGMA Symmetry Integrability Geom. Methods Appl. 12
, 083, 20pp (2016). DOI 10.3842/SIGMA.2016.083
- The SIAM 100-Digit Challenge: A Decade Later, Jahresber. Dtsch. Math.-Ver. 118
, pp. 87-123 (2016). DOI 10.1365/s13291-016-0137-2
. Errata
- 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).
- (with A. Its, S. Olver, G. Wechslberger) Numerical Methods for the Discrete Map \(Z^a\)
, in: A. Bobenko (Ed.), Advances in Discrete Differential Geometry
, Springer-Verlag, pp. 151-176 (2016). DOI 10.1007/978-3-662-50447-5_4
- A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge, Ann. Appl. Probab. 26
, pp. 1942-1946 (2016). DOI 10.1214/15-AAP1121
- (with P.J. Forrester) Singular values and evenness symmetry in random matrix theory, Forum Math. 28
; pp. 873-891 (2016). DOI 10.1515/forum-2015-0055
- (with M. La Croix) The singular values of the GOE, Random Matrices Theory Appl. 4
, 1550009, 32pp (2015). DOI 10.1142/S2010326315500094
- (with G. Wechslberger) Automatic deformation of Riemann-Hilbert problems with applications to the Painlevé II transcendents, Constr. Approx. 39
, pp. 151-171 (2014). DOI 10.1007/s00365-013-9199-x
- (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
, pp. 1799-1822 (2013). DOI 10.1088/0951-7715/26/6/1799
.
- (with G. Wechslberger) Optimal Contours for High-Order Derivatives, IMA J. Numer. Anal. 33
, pp. 403-412 (2013). DOI 10.1093/imanum/drs030
.
- (with S. Xiang) On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity, SIAM J. Numer. Anal. 50
, pp. 2581-2587 (2012). DOI 10.1137/120869845
. Zbl. 1259.65059.
- Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals. Found. Comput. Math. 11
, pp. 1-63 (2011). DOI 10.1007/s10208-010-9075-z
. MR 2012a:65061; Zbl. 1213.65039.
- On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review. Markov Processes Relat. Fields 16
, pp. 803-866 (2010). MR2895091, Zbl. 1222.60013.
- Asymptotic Independence of the Extreme Eigenvalues of GUE. J. Math. Phys. 51
, 023514, 8pp. (2010). DOI 10.1063/1.3290968
. MR 2011b:82038.
- On the Numerical Evaluation of Fredholm Determinants. Math. Comp. 79
, pp. 871-915 (2010). DOI 10.1090/s0025-5718-09-02280-7
. MR 2011b:65069; Zbl. 1208.65182. Erratum
- (with T. A. Driscoll and L. N. Trefethen) The Chebop System for Automatic Solution of Differential Equations. BIT 48
, pp. 701-723 (2008). DOI 10.1007/s10543-008-0198-4
. MR 2009j:65381; Zbl. 1162.65370.
- (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
, pp. 405-415 (2008). DOI 10.1007/s10955-008-9621-0
. MR 2009j:60214; Zbl. 1161.82340.
- (with T. März) Fast Image Inpainting Based on Coherence Transport. J. Math. Imaging Vis. 28
, pp. 259-278 (2007). DOI 10.1007/s10851-007-0017-6
. Because the publisher has corrupted the image quality: version with high quality images. MR 2367298.
- (with T. Schmelzer) Taming a Hydra of Singularities. Amer. Math. Monthly 114
, pp. 727-732 (2007). MR 2354442; Zbl 1154.26012.
- A Model for Understanding Numerical Stability. IMA J. Numer. Anal. 27
, pp. 219-231 (2007). DOI 10.1093/imanum/drl037
. MR 2008c:65122; Zbl. 1114.65041.
- (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.
- (with C. Rasch) Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle. Comput. Visual Sci. 9
, pp. 57-69 (2006). DOI 10.1007/s00791-006-0016-y
. MR 2007c:65102.
- (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.
- (with A. Schiela) Sparsing in Real Time Simulation. Z. angew. Math. Mech. 83
, pp. 637-647 (2003). MR 2004j:65107; Zbl. 1032.65089.
- Normen zur Charakterisierung der schwach*-Konvergenz beschränkter Folgen. Math. Semesterber. 48
, pp. 247-260 (2002). MR 2003h:46030; Zbl. 1032.46010.
- 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
.
- (with C. Schütte) Adaptive Accuracy Control of Car-Parrinello Simulations. Numer. Math. 83
, pp. 179-186 (1999). MR 2000e:65122; Zbl. 933.81005.
- (with C. Schütte) On the Singular Limit of the Quantum-Classical Molecular Dynamics Model. SIAM J. Appl. Math. 59
, pp. 1208-1224 (1999). MR 2000c:81067; Zbl. 926.34073.
- (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.
- (with M. Schemann) An Adaptive Rothe Method for the Wave Equation. Comput. Visual Sci. 1
, pp. 137-144 (1998). Zbl. 915.65105.
- (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.
- (with C. Schütte) A Mathematical Investigation of the Car-Parrinello Method. Numer. Math. 78
, pp. 359-376 (1998). MR 99d:81183; Zbl. 887.34026.
- (with C. Schütte) Homogenization Approach to Smoothed Molecular Dynamics. Nonlinear Analysis 30
, pp. 1805-1814 (1997). MR 99b:70016; Zbl. 920.70018.
- (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.
- (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).
- (with P. Nettesheim, B. Schmidt, C. Schütte) An Explicit and Symplectic Integrator for Quantum-Molecular Dynamics. Chem. Phys. Lett. 256, pp. 581-588 (1996).
- (with P. Nettesheim, C. Schütte) Quantum-classical Molecular Dynamics as an Approximation to Full Quantum Dynamics. J. Chem. Phys. 105, pp. 1074-1083 (1996).
- (with P. Deuflhard) The Cascadic Multigrid Method for Elliptic Problems. Numer. Math. 75
, pp. 135-152 (1996). MR 98a:65175; Zbl. 873.65107.
- (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.
- 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.
- 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.
- (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.
- (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.
- 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).
- 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.
- 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.
- 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
- Modern Aspects of Random Matrix Theory (V. Vu ed.), SIAM Rev. 57, pp. 632-634 (2015).
- 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
- (with S. Wagon) A perplexing polynomial puzzle, revisited. College Math. J. 36, p. 288 (2005).
- (with G. Ziegler) Die Beweise des Sommers. Mitteilungen der DMV 12, pp. 181-183 (2004).
- PRIMES Is in P: A Breakthrough for "Everyman"
. 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
, pp. 55-62 (2008).
- French translation: PRIMES is in P, une avancée accessible à «l'homme ordinaire». Gazette des Mathématiciens 98
, pp. 14-29 (2003). Translation by Colette Anné. Zbl. 1067.11079.
Unpublished Notes & Papers
- On Hathaway's circular pursuit problem, (April 2011).
- On Bellman's linear search problem, (March 2010).
- (with W. Boiger) Local Morphological Schemes for the Affine Morphological Scale Space. Preprint, 17pp, Technische Universität München (March 2006).
- An Experimental Approach to the Singular Modulus k100, (March 2005).
- How Mathematica and Maple Get Meijer's G-function into Definite Integrals, (February 2005).
- Solution of a Problem Posed by Jörg Waldvogel, (July 2003).
- Short Remarks on the Solution of the SIAM 100-digit Challenge, (May 2002).
- Zur Eindeutigkeit der Viskositätslösungen beim Cauchy-Problem von Hamilton-Jacobi Gleichungen, (October 2000).
- Homogenization in Time II: Mechanical Systems Subject to Friction and Gyroscopic Forces. SC-97-65
, Konrad-Zuse-Zentrum Berlin (1997).
- A Note on the Adiabatic Theorem of Quantum Mechanics, (August 1997).
- On Microlocal Obstructions to the Compactness of Sequences, (September 1996).
- (with C. Schütte) A Mathematical Approach to Smoothed Molecular Dynamics: Correcting Potentials for Freezing Bond Angles. SC 95-30
, Konrad-Zuse-Zentrum Berlin (1995).
- On the Convergence of Cascadic Iterations for Elliptic Problems. SC 94-08
, Konrad-Zuse-Zentrum Berlin (1994).
- Die Maximalwinkelbedingung für Finite Elemente, (December 1993).
- A Sharpened Condition Number Estimate for the BPX Preconditioner of Elliptic Finite Element Problems on Highly Nonuniform Triangulations. SC 91-09
, Konrad-Zuse-Zentrum Berlin (1991).
- (with B. Erdmann, R. Roitzsch) KASKADE: Numerical Experiments. TR 91-01
, Konrad-Zuse-Zentrum Berlin (1991).
Unpublished Lecture Notes
- Quantenrechnen (Quantum Computation)
, Technische Universität München (2003).
Theses
- 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.
- An Adaptive Multilevel Approach for Parabolic Equations in Two Space Dimensions. Dissertation, Freie Universität Berlin, 136pp; published as TR 91-07
, Konrad-Zuse-Zentrum Berlin (1991).
- Adaptive Multilevel Discretization in Time and Space for Parabolic Partial Differential Equations. Diplomarbeit, Freie Universität Berlin, 75pp; published as TR 89-07
, Konrad-Zuse-Zentrum Berlin (1989).
Pauca sed Matura. Johann Carl Friedrich Gauß