Institut für Zuverlässiges Rechnen
Leiter:
Prof. Dr. Siegfried M. Rump
PUBLIKATIONEN - MARKO LANGE
- F. Bünger, M. Lange, and S.M. Rump. On norms of principal submatrices. Linear Algebra and its Applications (LAA), 620:27–36, 2021. ( doi:10.1016/j.laa.2021.02.021)
- M. Lange. Verification methods for conic linear programming problems. Special Section on Verified Numerical Computations, Part I, Volume 11 Issue 3, 327–358, 2020. (doi:10.1587/nolta.11.327)
- M. Lange and S.M. Rump. Faithfully rounded floating-point computations. ACM transactions on mathematical software, 46(3), 2020. (doi:10.1145/3290955)
- R. Kobayashi, M. Lange, A. Minamihata, and S.M. Rump. Verified Inclusion of a Basis of the Null space. Reliable Computing, 27:26–41, 2020. (PDF) (hdl.handle.net/11420/7807)
- M. Lange and S.M. Rump. Verified inclusions of a nearest matrix of specified rank deficiency via a generalization of Wedin's sin (θ) theorem [winner of the Moore prize 2021]. BIT Numerical Mathematics, 61:361–380, 2021. (PDF) (doi:10.1007/s10543-020-00827-y)
- M. Lange and S. Oishi. A note on Dekker’s FastTwoSum algorithm. Numerische Mathematik, 145:383–403, 2020. (doi:10.1007/s00211-020-01114-2)
- D. Chaykin, C. Jansson, F. Keil, M. Lange, K.T. Ohlhus, and S.M. Rump. Rigorous Lower Bounds for the Ground State Energy of Molecules by Employing Necessary N-Representability Conditions. Journal of Chemical Theory and Computation, 2020. (doi:10.1021/acs.jctc.0c00497)
- M. Lange and S.M. Rump. Sharp estimates for perturbation errors in summations. Math. of Comp., 88:349–368, 2019. (PDF) (doi:10.1090/mcom/3355)
- M. Lange and S.M. Rump. Error estimates for the summation of real numbers with application to floating-point summation. BIT, 57:927–941, 2017. (PDF) (doi:10.1007/s10543-017-0658-9)
- S.M. Rump and M. Lange. On the Definition of Unit Roundoff. BIT Numerical Mathematics, 56(1):309–317, 2015. (PDF) (doi:10.1007/s10543-015-0554-0)
- M. Lange. A New Matrix Splitting Based Relaxation for the Quadratic Assignment Problem. MACIS: Mathematical Aspects of Computer and Information Sciences, 535–549, 2015. (doi:10.1007/978-3-319-32859-1_45)
- M. Lange. Residual bounds for some or all singular values. Linear Algebra and its Applications, 464:28–37, 2015. (doi:10.1016/j.laa.2013.06.023)
- M. Lange. mail to the Reliable computing mailing list, October 2012.