INTLAB

INTLAB (Interval Laboratory)
Oreeginal author(s)	S.M. Rump
Developer(s)	S.M. Rump; Cleve Moler; Shinichi Oishi etc.
Written in	MATLAB/GNU Octave
Operatin seestem	Unix, Microsoft Windows, macOS
Available in	English
Teep	Numerical analysis; Validatit numerics; Numerical linear algebra; Integral (Numerical integration); Numerical methods for ordinary differential equations etc.
Website	www.ti3.tu-harburg.de/rump/intlab/

INTLAB (INTerval LABoratory) is an interval arithmetic library usin MATLAB^[1]^[2]^[3]^[4]. INTLAB wis usit tae develop other MATLAB-basit libraries such as VERSOFT^[5] an INTSOLVER^[6], an it wis usit tae solve some problems i the " Hundred-dollar, Hundred-digit Challenge problems"^[7].

Version history eedit

12/30/1998 Version 1
03/06/1999 Version 2
11/16/1999 Version 3
- 03/07/2002 Version 3.1
12/08/2002 Version 4
- 12/27/2002 Version 4.1
- 01/22/2003 Version 4.1.1
- 11/18/2003 Version 4.1.2
04/04/2004 Version 5
- 06/04/2005 Version 5.1
- 12/20/2005 Version 5.2
- 05/26/2006 Version 5.3
- 05/31/2007 Version 5.4
- 11/05/2008 Version 5.5
05/08/2009 Version 6
12/12/2012 Version 7
- 06/24/2013 Version 7.1
05/10/2014 Version 8
01/22/2015 Version 9

Works citit bi INTLAB eedit

INTLAB is basit on the previous studies o the main author, includin his works wi co-authors.

S. M. Rump: Fast and Parallel Interval Arithmetic, BIT Numerical Mathematics 39(3), 539–560, 1999.
S. Oishi, S. M. Rump: Fast verification of solutions of matrix equations, Numerische Mathematik 90, 755–773, 2002.
T. Ogita, S. M. Rump, and S. Oishi. Accurate Sum and Dot Product, SIAM Journal on Scientific Computing (SISC), 26(6):1955–1988, 2005.
S.M. Rump, T. Ogita, and S. Oishi. Fast High Precision Summation. Nonlinear Theory and Its Applications (NOLTA), IEICE, 1(1), 2010.
S.M. Rump: Ultimately Fast Accurate Summation, SIAM Journal on Scientific Computing (SISC), 31(5):3466–3502, 2009.
S.M. Rump, T. Ogita, and S. Oishi: Accurate Floating-point Summation I: Faithful Rounding. SIAM Journal on Scientific Computing (SISC), 31(1): 189–224, 2008.
S. M. Rump, T. Ogita, and S. Oishi: Accurate Floating-point Summation II: Sign, K-fold Faithful and Rounding to Nearest. SIAM Journal on Scientific Computing (SISC), 31(2):1269–1302, 2008.
S. M. Rump: Ultimately Fast Accurate Summation, SIAM Journal on Scientific Computing (SISC), 31(5):3466–3502, 2009.
S. M. Rump. Accurate solution of dense linear systems, Part II: Algorithms using directed rounding. Journal of Computational and Applied Mathematics (JCAM), 242:185–212, 2013.
S. M. Rump. Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM Journal of Matrix Analysis and Applications (SIMAX), 33(1):130–148, 2012.
S. M. Rump: Improved componentwise verified error bounds for least squares problems and underdetermined linear systems, Numerical Algorithms, 66:309–322, 2013.
R. Krawzcyk, A. Neumaier: Interval slopes for rational functions and associated centered forms, SIAM Journal on Numerical Analysis 22, 604–616 (1985)
S. M. Rump: Expansion and Estimation of the Range of Nonlinear Functions, Mathematics of Computation 65(216), pp. 1503–1512, 1996.

External links eedit

INTLAB Archived 2020-01-30 at the Wayback Machine
List of INTLAB contributors Archived 2020-08-06 at the Wayback Machine
VERSOFT
INTSOLVER

References eedit

↑ ^a ^b ^c ^d ^e S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.
↑ ^a ^b ^c Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics.
↑ ^a ^b ^c ^d ^e Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287–449.
↑ ^a ^b ^c Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).
↑ Rohn, J. (2009). VERSOFT: verification software in MATLAB/INTLAB.
↑ Montanher, T. M. (2009). Intsolver: An interval based toolbox for global optimization. Version 1.0.
↑ Bornemann, F., Laurie, D., & Wagon, S. (2004). The SIAM 100-digit challenge: a study in high-accuracy numerical computing. Society for Industrial and Applied Mathematics.
↑ Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.

[rump-1] S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.

[moore-2] Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics.

[acta-3] Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287–449.

[har-4] Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).

[5] Rohn, J. (2009). VERSOFT: verification software in MATLAB/INTLAB.

[6] Montanher, T. M. (2009). Intsolver: An interval based toolbox for global optimization. Version 1.0.

[7] Bornemann, F., Laurie, D., & Wagon, S. (2004). The SIAM 100-digit challenge: a study in high-accuracy numerical computing. Society for Industrial and Applied Mathematics.

[8] Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.

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