フォルクマール・ボルネマン

フォルクマール・ボルネマンは数値解析を専門とするドイツの数学者であり、数値線形代数や常微分方程式の数値解法に関する著書で知られている。

1. 著書
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Folkmar Bornemann: Homogenization in Time of Singularly Perturbed Mechanical Systems. Springer, Berlin 1998, ISBN 978-3-540-64447-7.
Peter Deuflhard, Folkmar Bornemann: Scientific Computing with Ordinary Differential Equations. Springer, New York 2002, ISBN 978-0-387-21582-2.
Bornemann, F., Laurie, D., & Wagon, S. . The SIAM 100-digit challenge: a study in high-accuracy numerical computing. SIAM.
Bornemann, F. . Numerical linear algebra: a concise introduction with MATLAB and Julia. Springer.

2. 代表的な論文
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2.1. 単著
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2.1.1. 1990年代
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An adaptive multilevel approach to parabolic equations I. General theory and 1D implementation, FA Bornemann - Impact of computing in science and engineering, 1990.
An adaptive multilevel approach to parabolic equations: II. variable-order time discretization based on a multiplicative error correction, FA Bornemann - IMPACT of Computing in Science and Engineering, 1991.
An adaptive multilevel approach to parabolic equations III. 2D error estimation and multilevel preconditioning, FA Bornemann - IMPACT of Computing in Science and Engineering, 1992.

2.1.2. 2009年-2019年
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On the numerical evaluation of distributions in random matrix theory: a review, F Bornemann - arXiv preprint arXiv:0904.1581, 2009.
On the numerical evaluation of Fredholm determinants, F Bornemann - :en:Mathematics of Computation, 2010.
Bornemann, F. . Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals. Foundations of Computational Mathematics, 11, 1-63.
Bornemann, F. . The SIAM 100-digit challenge: a decade later. Jahresbericht der Deutschen Mathematiker-Vereinigung, 118, 87-123.

2.2. 共著
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2.2.1. 1990年代
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A basic norm equivalence for the theory of multilevel methods, F Bornemann, H Yserentant - :en:Numerische Mathematik, 1993.
Bornemann, F., Erdmann, B., & Kornhuber, R. . Adaptive multivlevel methods in three space dimensions. International journal for numerical methods in engineering, 36, 3187-3203.
The cascadic multigrid method for elliptic problems, FA Bornemann, P Deuflhard - :en:Numerische Mathematik, 1996.
A posteriori error estimates for elliptic problems in two and three space dimensions, FA Bornemann, B Erdmann, R Kornhuber - :en:SIAM Journal on Numerical Analysis, 1996.
An explicit and symplectic integrator for quantum-classical molecular dynamics, P Nettesheim, FA Bornemann, B Schmidt, C Schütte - Chemical Physics Letters, 1996.
Homogenization of Hamiltonian systems with a strong constraining potential, FA Bornemann, C Schütte - Physica D: Nonlinear Phenomena, 1997.
A mathematical investigation of the Car-Parrinello method, FA Bornemann, C Schütte - :en:Numerische Mathematik, 1998.

2.2.2. 2000年代
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Schiela, A., & Bornemann, F. . Sparsing in real time simulation. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, 83, 637-647.
Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle, F Bornemann, C Rasch - Computing and Visualization in Science, 2006.
The chebop system for automatic solution of differential equations, TA Driscoll, F Bornemann, LN Trefethen - :en:BIT Numerical Mathematics, 2008.

2.2.3. 2010年代
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Xiang, S., & Bornemann, F. . On the convergence rates of Gauss and Clenshaw-Curtis quadrature for functions of limited regularity. :en:SIAM Journal on Numerical Analysis, 50, 2581-2587.

3. 関連項目
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INTLAB 
:en:Chebfun 
ニック・トレフェセン  
ペーター・ドイフルハード 

4. 外部リンク
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