Forschungsbericht 2005

4-04 Zuverlässiges Rechnen

Programmiersprachen und Algorithmen

Forschungsprojekte

• E.4-04.023 Funktechnische Betriebsleitsysteme verteilter autonomer Fahrzeuge.
• E.4-04.024 Innovative Fahrgast-Informationssysteme im ÖPNV-Bus.
• E.4-04.025 Architektur und Entwurf von Numerik-Co-Prozessoren.
• E.4-04.031 Intervall Toolbox INTLAB
• E.4-04.032 Fahrzeugleitsysteme im Bereich Logistikmanagement und Tourenplanung
• E.4-04.033 Netzwerkdesign von Wasserverteilungssystemen
• E.4-04.034 Flexible rekonfigurierbare Multiprozessor-Architekturen
• E.4-04.035 Koprozessorarchitektur basierend auf speichergekoppelten Prozessoren
• E.4-04.036 Ein konfigurierbares Betriebsleitsystem für Bahnen.
• E.4-04.037 Self-validating methods.
• E.4-04.038 Fast Summation and Dot Product.

Kooperationen

• Bombardier, Braunschweig.
• DB Systems, Frankfurt.
• Daimler-Benz, Esslingen.
• Emagic, Hamburg.
• IBM Forschung und Entwicklung, Böblingen.
• IMPA, Rio de Janeiro, Brasilien.
• Prof. Dr. Arnold Neumaier, Universität Wien, Österreich.
• Prof. Dr. Jiri Rohn, Katedra Aplikovane Matematiky Matematicko-Fyzikalui Fakulta, Univerzity Karlovy, Czech Republic.
• Prof. Dr. Jürgen Garloff, Fachbereich Informatik, Fachhochschule Konstanz.
• Prof. Dr. Michael Plum, Inst.f. Mathematik, Universität Karlsruhe.
• Prof. Dr. Mitsuhiro Nakao, Kyushu University, Fukuoka, Japan.
• Prof. Dr. Shin'ichi Oishi, Waseda University, Tokio, Japan.
• RMS Hamburg.
• Universidade Federal Pernambuco (UFPE) in Recife, Brasilien.
• Universidade Federal Rio Grande do Sul (UFRGS) in Porto Alegre, Brasilien.

Publikationen

Veröffentlichungen

• 4-04.054V
  C. Jansson. An Interval Method for Global Unconstrained Optimization, Operations Research 91, eds., P. Gritzmann, R. Hettich, R. Horst, E. Sachs, Physica-Verlag, 102-105, 1991.
• 4-04.055V
  S. M. Rump. On the Solution of Interval Linear Systems, COMPUTING 47, 337-353 (1992).
• 4-04.056V
  S. M. Rump. Inclusion of the Solution of Large Linear Systems with Positive Definite Symmetric M-Matrix, Proceedings SCAN 91 Oldenbourg, North-Holland Amsterdam, 339-350 (1992).
• 4-04.057V
  S. M. Rump. Inclusion of the Solution of Large Linear Systems with M-Matrix, Interval Computations, Nr. 1(3), 22-43, (1992).
• 4-04.058V
  D. Claudio, S. M. Rump. Inclusion Methods for Real and Complex Functions in one Variable, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 92.5, März 1992.
• 4-04.059V
  S. M. Rump. Zur Außen- und Inneneinschließung von Eigenwerten bei toleranzbehafteten Matrizen, ZAMM 73 Nr. 6, (1992).
• 4-04.060V
  S. M. Rump. Accuracy Control and Estimation, Self-Validating Systems and Software Environments for Scientific Computation, eds., P. Gaffney, E. Houstis, IFIP Transactions on Programming Environments for High-Level Scientific Problem Solving, North-Holland Amsterdam, 49-56 (1992).
• 4-04.061V
  S. M. Rump. Recent Results in Interval Mathematics, Proceedings 5th International Conference on Scientific Computing, Benin City Nigeria (1992).
• 4-04.062V
  S. M. Rump. Symbolic, Algebraic and Validated Numerical Computation, Dagstuhl Seminar Report 43(92-32) (1992).
• 4-04.063V
  S. M. Rump. Validated Solution of Large Linear Systems, COMPUTING Supplementum, 191-213 (1993).
• 4-04.064V
  D. Claudio, S. M. Rump. GANA - Guaranteed Accuracy for Numerical Algorithms, Proceedings of the German Brazilian Workshop on Information Technology, Berlin, (1993).
• 4-04.065V
  Th. Teufel, et al. Grundlagenuntersuchung eines Expertensystems zur Diagnose einer regenerativen CO2-Bindungsanlage, BMFT Statusseminar, Automatisierungstechnologien für die Raumfahrt, (1992).
• 4-04.066V
  R. Lindemann. Schätzung von Kundenverhalten mittels neuronaler Netze, Diplomarbeit, TU Hamburg-Harburg, März 1993.
• 4-04.067V
  C. Jansson. A Global Optimization Method Using Interval Arithmetic, Computer Arithmetic and Enclosure Methods, eds., L. Atanassova, J. Herzberger, IMACS 1992, Elsevier Science Publisher B.V., 259-267.
• 4-04.068V
  C. Jansson, O. Knüppel. Eine intervallanalytische Methode für globale Optimierungsprobleme, ZAMM, 73(1993)6, 805-807.
• 4-04.069V
  C. Jansson, O. Knüppel. A Minimization Method for Systems with Singular Value Constraints, Operations Research 92, eds., A. Karmann, K. Mosler, M. Schrader, G. Uebe, Physica-Verlag, 190-192, 1993.
• 4-04.071V
  C. Jansson. On Self-Validating Methods for Optimization Problems, Topics in Validated Computations, ed. J. Herzberger, North-Holland ( ELSEVIER), 381-439, 1994.
• 4-04.072V
  Th. Teufel, et al. C^2 Compiler Concepts, Springer-Verlag Wien, Berlin, 1993.
• 4-04.073V
  O. Knüppel. BIAS - Basic Interval Arithmetic Subroutines, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 93.3, Juli 1993.
• 4-04.074V
  O. Knüppel. PROFIL - Programmers Runtime Optimized Fast Interval Library, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 93.4, Juli 1993.
• 4-04.075V
  O. Knüppel, T. Simenec. PROFIL/BIAS Extensions, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 93.5, November 1993.
• 4-04.076V
  O. Knüppel. A Multiple Precision Arithmetic for PROFIL, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 93.6, November 1993.
• 4-04.077V
  C. Jansson, S.M. Rump. Algorithmen mit Ergebnisverifikation - einige Bemerkungen zu neueren Entwicklungen, Jahrbuch überblicke Mathematik 1994, 47-73.
• 4-04.078V
  S.M. Rump. Verified Solution of Large Systems and Global Optimization Problems, Proceeding of the Conference Linear/Nonlinear Iterative Methods and Verification of Solution, Ehime University, Matsuyama, Japan (1994).
• 4-04.079V
  O. Knüppel. PROFIL/BIAS - A Fast Interval Library, Computing, Vol. 53, 277-287, 1994.
• 4-04.080V
  C. Jansson, S.M. Rump. Self-Validating Methods, Some Recent Developments, Beiträge zur Angewandten Analysis und Informatik, E. Schock (editor), Shaker-Verlag, Aachen, 148-170, 1994.
• 4-04.081V
  C. Jansson. Some properties of Linear Interval Systems and Applications, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 94.3, 13 Seiten, 1994.
• 4-04.083V
  S.M. Rump. Improved Iteration Schemes for Validation Algorithms for Dense and Sparse Nonlinear Systems, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 95.1 März 1995.
• 4-04.084V
  S.M. Rump. Verified Solution of Large Systems and Global Optimization Problems. J. Comput. Appl. Math., 60:201-218, 1995.
• 4-04.085V
  R. Lindemann, S.M. Rump. COX - C with Operator eXtension, ICIAM 95 Proceedings.
• 4-04.086V
  Th. Teufel, et al. Genauer und trotzdem schneller - Ein neuer Coprozessor für hochgenaue Matrix- und Vektoroperationen, Elektronik, Heft 26 , 1994, Franzis-Verlag, München.
• 4-04.087V
  S. Kwee, Th. Teufel. A numerical Module for Computation with Verified Results, Proceedings of ICIAM 1995, Hamburg, Akademic-Verlag Berlin.
• 4-04.088V
  S.M. Rump. Improved Iteration Schemes for Validation Algorithms for Dense and Sparse Nonlinear Systems. Computing, 57(1):77-84, 1996.
• 4-04.089V
  S.M. Rump. Verified Solution of Large Linear and Nonlinear Systems. In H. Bulgak and C. Zenger, editors, Error Control and adaptivity in Scientific Computing, pages 279-298. Kluwer Academic Publishers, 1999.
• 4-04.091V
  S.M. Rump. The determinant of the sum of two matrices, (zur Veröffentlichung eingereicht).
• 4-04.092V
  S.M. Rump. Bounds for the Componentwise Distance to the Nearest Singular Matrix, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 95.3 1995.
• 4-04.093V
  S.M. Rump. Sharp lower and upperbounds for the Perron root of a nonnegative matrix, (zur Veröffentlichung eingereicht).
• 4-04.094V
  S.M. Rump. Perron-Frobenius like Theorems for not Sign-Restricted Matrices, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 95.5 1995.
• 4-04.095V
  S.M. Rump. Almost Sharp Bounds for the Componentwise Distance to the Nearest Singular Matrix, Berichte des Forschungsschwerpunktes Informations- und Kommunikationstechnik, TU Hamburg-Harburg, Nr. 95.6 1995.
• 4-04.096V
  C. Jansson. On Applications of Self-Validating Methods in Optimization, ZAMM 75, 423-424,1995.
• 4-04.097V
  C. Jansson, O. Knüppel. A Branch-and-Bound Algorithm for Bound Constrained Optimization Problems without Derivatives, Journal of Global Optimization 7:297-331, 1995.
• 4-04.098V
  O. Knüppel. PROFIL/BIAS - Eine schnelle Intervallbibliothek, Zeitschrift für angewandte Mathematik und Mechanik, 75: SII529 - SII530, 1995.
• 4-04.099V
  S.M. Rump. Verified Computation of the Solution of Large Sparse Linear Systems, ZAMM 75, S439-442, (1995).
• 4-04.100V
  S.M. Rump. Verification Methods for Dense and Sparse Systems of Equations, in "Topics in Validated Computations - Studies in Computational Mathematics", ed. J. Herzberger, Elsevier Publications, 63-136, (1994).
• 4-04.101V
  S.M. Rump. Verified Solution of Large Systems and Global Optimization Problems, Journal of Computational and Applied Mathematics, 60, 201-218 (1995).
• 4-04.102V
  S.M. Rump. Expansion and Estimation of the Range of Nonlinear Functions, Mathematics of Computation, Vol. 65(216), 1503-1512 (1996).
• 4-04.103V
  S.M. Rump. Improved Iteration Schemes for Validation Algorithms for Dense and Sparse Nonlinear Systems, Computing 57(1) 77-84 (1996).
• 4-04.104V
  S.M. Rump, R. Lindemann. COX - C with Operator eXtension, Proceedings of the ICIAM World Congress, Hamburg (1996).
• 4-04.105V
  S.M. Rump. The distance between regularity and strong regularity, in "Scientific Computing and Validated Numerics", ed. G. Alefeld, A. Frommer and B. Lang, Mathematical Research, Volume 90, Akademie Verlag, 105-117 (1996).
• 4-04.106V
  S.M. Rump. Software Engineering im Scientific Computing, herausgegeben mit W. Mackens, Vieweg Verlag, 315 Seiten (1996).
• 4-04.108V
  T. Teufel, A. Pierick. Codierung von Daten für die sichere Mobilfunkübertragung, Signal+Draht, Heft Mai 1996.
• 4-04.109V
  T. Teufel. A Novel VLSI Vector Arithmetic Coprocessor for Advanced DSP Applicatios, Proceedings of ICSPAT 1996, Boston USA, Oktober 1996.
• 4-04.110V
  C. Jansson. Calculation of Exact Bounds for the Solution Set of Linear Interval Systems, Linear Algebra and its Applications, 251:321-340 (1997).
• 4-04.111V
  S.M. Rump. Inclusion of zeros of nowhere differentiable n-dimensional functions, Reliable Computing, 3(1), 5-16 (1997).
• 4-04.112V
  S.M. Rump. Bounds for the Componentwise Distance to the Nearest Singular Matrix, SIAM Journal Matrix Anal. Appl., Volume 18, Number 1, 83-103 (1997).
• 4-04.113V
  S.M. Rump. Theorems of Perron-Frobenius type for matrices without sign restrictions. Linear Algebra and its Applications (LAA), 266:1-42, 1997.
• 4-04.114V
  S.M. Rump. Almost Sharp Bounds for the Componentwise Distance to the Nearest Singular Matrix, Linear and Multilinear Algebra 42, 93-107 (1997).
• 4-04.115V
  S.M. Rump. Interval Arithmetic and Fuzzy Logic. In Proc. of the International NAISO congress on Information Science Innovations (ISI'2001), Dubai, pages 379-386, 2001.
• 4-04.116V
  S.M. Rump. Structured Perturbations and Symmetric Matrices, Linear Algebra and its Applications, Linear Algebra and its Applications, 278:121-132 (1997).
• 4-04.117V
  S.M. Rump. HARDY - High-Accuracy Arithmetic Applied to Dimensional Metrology, Proceedings of the 4th German-Brazilian Workshop on Information Technology, Berlin, 9-12 (1997).
• 4-04.118V
  T. Teufel, S. Kwee. Pipeline Optimisation for 32 bit Floatingpoint Units, Proceedings of ICSPAT 1997, San Diego, Sept. 1997.
• 4-04.119V
  T. Teufel. Neuer Fahrerarbeitsplatz im ÖPHV-Bus. International Union of Public Transport UIIP, Juni 1997.
• 4-04.120V
  P. Batra. Improvement of a convergence condition for the Durand-Kerner iteration, Journal of Computational and Applied Mathematics 96 :117-125 (1998).
• 4-04.121V
  C. Jansson. Construction of Convex Lower and Upper Bound Functions, Berichte desForschungsschwerpunktes Informations-und Kommunikationstechnik, Nr. 98.1, 17 Seiten, 1998.
• 4-04.122V
  C. Jansson. An NP-Hardness Result for Nonlinear Systems, Berichte des Forschungsschwerpunktes Informations-und Kommunikationstechnik, Nr. 97.3, 5 Seiten, 1997, und in: RELIABLE COMPUTING 4:345-350 (1998).
• 4-04.123V
  C. Jansson. Convex-Concave Extensions and Applications, SCAN98: IMACS/GAMM International Symposium On Scientific Computing, Computer Arithmetic and Validated Numerics, 61-63 (1998).
• 4-04.124V
  S.M. Rump. The sign-real spectral radius and cycle products, Linear Algebra and its Applications, 279:177-180 (1998).
• 4-04.125V
  S.M. Rump, D. Dennis und V. Kreinovich. Intervals and the Origins of Calculus, Reliable Computing 4, No. 2, 1-7 (1998).
• 4-04.126V
  S.M. Rump. A Note on Epsilon Inflation, Reliable Computing 4, No. 3, 1-5 (1998).
• 4-04.128V
  C. Jansson, J.Rohn. An Algorithm for Checking Regularity of Interval Matrices, SIAM J. Matrix ANAL. APPL., Vol. 20, No. 3, 756-776, 1999.
• 4-04.129V
  C. Jansson. Convex Relaxations for Global Constrained Optimization Problems, Scientific Computing in Chemical Engineering II, eds. F. Keil, W. Mackens, H. Voss, J. Werther, Springer-Verlag, Berlin, 322-329, 1999.
• 4-04.130V
  C. Jansson. Interval Linear Systems, in ENCYCLOPEDIA OF OPTIMIZATION, Vol. III, eds.: C.A. Floudas, P.M. Pardalos, Kluwer Academic Publishers, 69-76, 2001.
• 4-04.131V
  C. Jansson. Convex-Concave Extensions, BIT Vol. 40, No. 2, 291-313, 2000.
• 4-04.132V
  C. Jansson. Quasiconvex Relaxations Based on Interval Arithmetic, Linear Algebra and its Applications, 324, 27-53, 2001.
• 4-04.133V
  C. Jansson. Quasi Convex-Concave Extensions, in Symbolic Algebraic Methods and Verifikation Methods, eds.: G. Alefeld, J. Rohn, S.M. Rump, T. Yamamoto, Springer-Verlag Wien, 117-128, 2001.
• 4-04.134V
  S.M. Rump. INTLAB-INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77-104. Kluver Academic Publishers, 1999.
• 4-04.135V
  S.M. Rump. Interval computations with INTLAB. Brazilian Electronic Journal on Mathematics of Computation, Vol.1, 1999.
• 4-04.136V
  S.M. Rump. Ill-conditionedness need not be componentwise near to ill-posedness for least squares problems. BIT, 39(1):143-151, 1999.
• 4-04.137V
  S.M. Rump. Ill-conditioned Matrices are componentwise near to singularity. SIAM Review, 41(1):102-112, 1999.
• 4-04.138V
  S.M. Rump. Fast and parallel interval arithmetic. BIT, 39(3):539-560, 1999.
• 4-04.139V
  S.M. Rump. Self-Validating Methods. Linear Algebra and its Applications 324, 3-13, 2001.
• 4-04.140V
  S.M. Rump. Rigorous and portable standard functions. BIT 41(3), 540-562, 2001.
• 4-04.141V
  S.M. Rump. Perron-Frobenius and distance to singularity. submitted for publication, 2000.
• 4-04.142V
  S.M. Rump. INTLAB-INTerval LABoratory. in Handbook of Computer Algebra, eds.: J. Grabmeier, E. Kaltofen, V. Weispfenning, 2001.
• 4-04.143V
  S.M. Rump. Fast Verification Algorithms in Matlab, in "Symbolic Algebraic Methods and Verification Methods", eds.: G. Alefeld, J. Rohn, T. Yamamoto, Springer Mathematics, 209-226, 2001.
• 4-04.144V
  S.M. Rump. Conservatism of the Circle Criterion - Solution of a problem posed by A. Megretski, IEEE Transactions on Automatic Control 46(10): 1605-1608, 2001.
• 4-04.145V
  S.M. Rump. Computational Error Bounds for Multiple or Nearly Multiple Eigenvalues. Linear Algebra and its Applications, 324, 209-226, 2001.
• 4-04.146V
  S.M. Rump. A simple application of interval arithmetic. Brazilian Electronic Journal on Mathematics of Computation (BEJMC), 2, 2000.
• 4-04.147V
  S. Oishi and S.M. Rump. Fast Verification of Solutions of Matrix Equations. Numerische Mathematik 90(4):755-773, 2002.
• 4-04.148V
  S.M. Rump. Perron-Frobenius Theory and Distance to Ill-Posedness, American Mathematical Monthly, to appear 2001.
• 4-04.149V
  S.M. Rump. Algorithms for Computing Validated Results. In J. Grabmeier, E. Kaltofen, and V. Weispfennig, editors, Computer Algebra Handbook, chapter 2.12.2, pages 110-112. Springer, 2003.
• 4-04.150V
  S.M. Rump. Perron-Frobenius Theory for Complex Matrices. Linear Algebra and its Applications (LAA), 363:251-273, 2003.
• 4-04.151V
  S.M. Rump. On P-Matrices, Linear Algebra and its Applications (LAA), 363:237-250, 2003.
• 4-04.154V
  S. M. Rump. Optimal scaling for p-norms and componentwise distance to singularity. IMA Journal of Numerical Analysis (IMAJNA), 23:1-9, 2003.
• 4-04.155V
  T. Teufel. Neue Telematik-Dienste im ÖPNV-Bus, IAA-Nutzfahrzeuge, 2002.
• 4-04.156V
  T. Teufel. Modular integrierter Bordrechner mit neuen Telematik-Diensten für den ÖPNV, Inno Trans 2002, Sept. 2002.
• 4-04.157V
  J. Garloff, C. Jansson, and A.P. Smith. Convex-Concave Extensions for Polynomials. In Proc. Workshop on Validated Computing, pages 73-75, El Paso, Texas, 2002. SIAM.
• 4-04.158V
  J. Garloff, C. Jansson, and A.P. Smith. Construction of Lower Bound Functions for Polynomials. Technical Report 0201, Informatik, Fachhochschule Konstanz, 2002.
• 4-04.159V
  J. Garloff, C. Jansson, and A.P. Smith. Affine Lower Bound Functions for Polynomials and their Use in Global Optimization. In Notes of the 1st International Workshop on Global Constrained Optimization and Constraint Satisfaction, 2002.
• 4-04.160V
  C. Jansson. Rigorous Error Bounds for the Optimal Value of Linear Programming Problems. In Bliek et al., editor, Global Optimization and Constraint Satisfaction, Notes of the 1st International Workshop on Global Constrained Optimization and Constraint Satisfaction, Valbonne-Sophia Antipolis, pages 59-70, 2003.
• 4-04.161V
  C. Jansson. A rigorous lower bound for the optimal value of convex optimization problems. Technical Report 03.1, Forschungsschwerpunkt Informations- und Kommunikationstechnik, TU Hamburg-Harburg, 2003. http://www.ti3.tu-harburg.de/report/03.1.ps
• 4-04.162V
  J. Garloff, C. Jansson, and A.P. Smith. Lower bound functions for polynomials. Journal of Computational and Applied Mathematics, 157:207-225, 2003.
• 4-04.163V
  J. Garloff, C. Jansson, and A.P. Smith. Inclusion isotonicity of convex-concave extensions for polynomials based on Bernstein expansion. Computing, 70:111-119, 2003.
• 4-04.164V
  A.C. Hailer and S.M. Rump. Hedge-Effektivität: Lösung des Problems der kleinen Zahlen. (Hedge Accounting nach FAS 133 bzw. IAS 39. Zeitschrift für das gesamte Kreditwesen, 56(2003)(11):599-603, 2003.
• 4-04.165V
  A.C. Hailer, F. Loch, and P. Stork. Basel II: Optimale Zuordnung von Sicherheiten auf Kredite. Zeitschrift für das gesamte Kreditwesen, 55(2002)(22):1202-1206, 2002.
• 4-04.166V
  S.M. Rump. On Nishi's conditions for the Omega-property. IEICE Transactions on Fundamentals Communications Electronics Information and Systems, E86(9):2357-2359, 2003.
• 4-04.167V
  S.M. Rump. Structured Perturbations Part I: Normwise Distances. SIAM J. Matrix Anal. Appl. (SIMAX), 25(1):1-30, 2003.
• 4-04.168V
  S.M. Rump. Structured Perturbations Part II: Componentwise Distances. SIAM J. Matrix Anal. Appl. (SIMAX), 25(1):31-56, 2003.
• 4-04.169V
  S.M. Rump. Ten methods to bound multiple roots of polynomials. J. of Computation and Applied Mathematics (JCAM), 156:403-432, 2003.
• 4-04.170V
  T. Ogita, S.M. Rump, and S. Oishi. Fast and Accurate Computation of Scalar Product. to appear, 2003.
• 4-04.171V
  S.M. Rump and J. Zemke. On eigenvector bounds.BIT, 43:823-837, 2004.
• 4-04.172V
  S.M. Rump. Computer assisted proofs and Self-Validating Methods, In B. Einarsson (ed.): Handbook on Acuracy and Reliability in Scientific Computation, SIAM publications, 53 pages. to appear, 2004.
• 4-04.174V
  C. Jansson. Rigorous Lower and Upper Bounds in Linear Programming. SIAM J. Optim., 14(3):914-935, 2004.
• 4-04.175V
  C. Jansson. A rigorous lower bound for the optimal value of convex optimization problems. J. Global Optimization, 28:121-137, 2004.
• 4-04.176V
  T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product with Applications. Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, pages 152-155, 2004.
• 4-04.177V
  T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product. to appear in SIAM Journal on Scientific Computing (SISC), 2004.
• 4-04.179V
  S.M. Rump. Computer-Assisted Proofs I. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(3):214-223, 2004.
• 4-04.180V
  S.M. Rump. Computer-Assisted Proofs II. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(4):44-57, 2004. translated by T. Ogita.
• 4-04.181V
  Chr. Keil. LURUPA -- Rigorose Fehlerschranken für Lineare Programme. Master's thesis, Technische Universität Hamburg-Harburg, 2004.
• 4-04.182V
  S.M. Rump and T. Ogita. Super-Fast Validated Solution of Linear Systems. accepted for publication in Journal of Computational and Applied Mathematics (JCAM), 2005.
• 4-04.183V
  S.M. Rump. INTLAB - Interval Laboratory, a Matlab toolbox for verified computations, Version 5.1, 2005.
• 4-04.184V
  S.M. Rump. High Precision Evaluation of Nonlinear Functions. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 733-736, 2005.
• 4-04.185V
  S.M. Rump. Eigenvalues, pseudospectrum and structured perturbations. Accepted for publication in Linear Algebra and its Applications (LAA), 2005.
• 4-04.186V
  S.M. Rump. Computer-assisted proofs and Self-Validating Methods. In B. Einarsson, editor, Handbook on Acuracy and Reliability in Scientific Computation, pages 195-240. SIAM, 2005.
• 4-04.187V
  K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. Componentwise Verified Solutions of Linear System Suited for Java. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 749-752, 2005.
• 4-04.188V
  K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. A Method of Obtaining Verified Solutions for Linear Systems suited for Java. accepted for publication in Journal of Computational and Applied Mathematics (JCAM), 2005.
• 4-04.189V
  T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems. Trans. JSIAM, 15(3):269-287, 2005.
• 4-04.190V
  T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Method for Dense Linear Systems with Arbitrariliy Ill-conditioned Matrices. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 745-748, 2005.
• 4-04.191V
  T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product. SIAM Journal on Scientific Computing (SISC), 26(6):1955-1988, 2005.
• 4-04.192V
  A.C. Hailer and S.M. Rump. Evaluierung von Hedge-Effektivitätstests. Zeitschrift für das gesamte Kreditwesen, 58(20):1089-1097, 2005.
• 4-04.193V
  A. Hailer and S.M. Rump. Evaluation of Hedge Effectiveness Tests. Journal of Derivatives Accounting (JDA), 2(1):31-52, 2005.
• 4-04.194V
  S. Friedland, D. Hershkowitz, and S.M. Rump. Positive entries of stable matrices. Electronic Journal of Linear Algebra (ELA), 12:17-24, 2005.
• 4-04.195V
  C. Jansson and C. Keil. Rigorous Error Bounds for the Optimal Value in Semidefinite Programming. 2005. Submitted, and electronically published http://www.optimization-online.org/DBHTML/2005/01/1047.html.
• 4-04.196V
  C. Jansson. Termination and Verification for Ill-posed Semidefinite Programming Problems, http://optimization-online.org/DBHTML/2005/06/1150.html, 2005.
• 4-04.197V
  C. Jansson. Rigorous Results in Combinatorial Optimization. Algebraic and Numerical Algorithms and Computer-assisted Proofs, 2005. 8 pages.
• 4-04.198V
  C. Jansson. On Verifed Computation in Combinatorial Optimization. International Symposium on Nonlinear Theory and its Applications (NOLTA2005), Bruges, Belgium, pages 717-717, 2005.
• 4-04.199V
  C. Keil and C. Jansson. Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library. Reliable Computing, 2006.

Dissertationen

• 4-04.001D
  O. Knüppel. Einschließungsmethoden zur Bestimmung der Nullstellen nichtlinearer Gleichungssysteme und ihre Implementierung, TUHH, 1995.
• 4-04.002D
  J.B. Oliveira. Slope methods for sharper interval inclusions and their application to global optimisation, TUHH, 1996.
• 4-04.003D
  R. Lindemann. COX-C mit Operatorkozept, TUHH, 1997.
• 4-04.004D
  P. Batra. Abschätzungen und Iterationsverfahren für Polynom-Nullstellen, TUHH, 1999.
• 4-04.005D
  T. Ringel. Analyse, Akquisition und Verarbeitung distribuiert vorliegenden Wissens zur Diagnose von Kraftfahrzeugsystemen, TUHH, 1999.
• 4-04.006D
  J. Zemke. Krylov Subspace Methods in Finite Precision: A Unified Approach, TUHH, 2003.

Habilitationen

• 4-04.001H
  C. Jansson. On Self-Validating Methods for Optimisitation Problems, Topics in Validated Computations, J. Herzberger (Editor), 1994 Elsevier Science B.V., 381-438, ISBN: 0 444 81 685 2.