Intervall Toolbox INTLAB
INTLAB ist eine Matlab Toolbox zur Berechnung sicherer Schranken für die Lösung numerischer Probleme. INTLAB ist rein in Matlab implementiert und durch das Operator Konzept leicht anwendbar. Durch spezielle Definition der Intervallarithmetik sind die Programme um ein bis zwei Größenordnungen schneller als herkömmliche Implementierungen. Die Toolbox wird laufend erweitert und steht momentan in Release 5 zur Verfügung. Die Software ist public domain und wird weltweit von mehreren tausend Wissenschaftlern, in über 40 Ländern eingesetzt. Publikationen - 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. - 4-04.138V
S.M. Rump. Fast and parallel interval arithmetic. BIT, 39(3):539-560, 1999. - 4-04.140V
S.M. Rump. Rigorous and portable standard functions. BIT 41(3), 540-562, 2001. - 4-04.142V
S.M. Rump. INTLAB-INTerval LABoratory. in Handbook of Computer Algebra, eds.: J. Grabmeier, E. Kaltofen, V. Weispfenning, 2001. - 4-04.146V
S.M. Rump. A simple application of interval arithmetic. Brazilian Electronic Journal on Mathematics of Computation (BEJMC), 2, 2000. - 4-04.167V
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. - 4-04.171V
S.M. Rump and J. Zemke. On eigenvector bounds.BIT, 43:823-837, 2004. - 4-04.182V
S.M. Rump and T. Ogita. Super-Fast Validated Solution of Linear Systems. Journal of Computational and Applied Mathematics (JCAM), 199(2):199-206, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004). - 4-04.183V
S.M. Rump. INTLAB - Interval Laboratory, a Matlab toolbox for verified computations, Version 5.1, 2005. - 4-04.185V
S.M. Rump. Eigenvalues, pseudospectrum and structured perturbations. Linear Algebra and its Applications (LAA), 413:567-593, 2006. - 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. - 4-04.191V
T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product. SIAM Journal on Scientific Computing (SISC), 26(6):1955-1988, 2005. - 4-04.204V
S.M. Rump. Verification of Positive Definiteness. BIT Numerical Mathematics, 46:433-452, 2006. - 4-04.205V
S.M. Rump. INTLAB - Interval Laboratory, the Matlab toolbox for verified computations, Version 5.3, 2006 - 4-04.222V
S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM), 26:1-29, 2009.
- 4-04.225V
T. Nishi, T. Ogita, S. Oishi, and S. M. Rump. A Method for the Generation of a Class of Ill-conditioned Matrices. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 53-56, 2008. - 4-04.231V
S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, 49(2):419-431, 2009. - 4-04.233V
S. M. Rump and S. Oishi. Verified Error Bounds for Double Roots of Nonlinear Equations. In 2009 International Symposium on Nonlinear Theory and its Applications, NOLTA'09, Sapporo, Japan, 2009. - 4-04.234V
S.M. Rump and S. Graillat. Verified error bounds for multiple roots of systems of nonlinear equations. Numerical Algorithms, 54(3):359-377, 2009. DOI 10.1007/s11075-009-9339-3. - 4-04.235V
S.M. Rump. Ultimately Fast Accurate Summation. SIAM Journal on Scientific Computing (SISC), 31(5):3466-3502, 2009. - 4-04.236V
S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM), 26:249-277, 2009. - 4-04.249V
S.M. Rump. A Model Problem for Global Optimization.In Nonlinear Theory and Its Appilcations (NOLTA), volume 1, pages 1-6. IEICE, 2010. - 4-04.251V
S.M. Rump. Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19:287-449, 2010. - 4-04.252V
S.M. Rump and S. Oishi. Verified computation of a disc containing exactly k roots of a univariate nonlinear function.Nonlinear Theory and Its Applications (NOLTA), E93-N(Vol. (10)), 2010.
Stichwörter - Einschließungen
- Intervalle
- Verifikation
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