View source for INTLAB

'''INTLAB (INTerval LABoratory)''' is an [[interval arithmetic]] library<ref name="rump">S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.</ref><ref name="moore">Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. [[Society for Industrial and Applied Mathematics]].</ref><ref name="acta">Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. [[Acta Numerica]], 19, 287–449.</ref><ref name="har">Hargreaves, G. I. (2002). Interval analysis in [[MATLAB]]. Numerical Algorithms, (2009.1).</ref> using [[MATLAB]] and [[GNU Octave]], available in [[Windows]] and [[Linux]], [[macOS]]. It was developed by S.M. Rump from [[Hamburg University of Technology]]. INTLAB was used to develop other MATLAB-based libraries such as VERSOFT<ref>Rohn, J. (2009). VERSOFT: verification software in [[MATLAB]]/INTLAB.</ref> and INTSOLVER,<ref>Montanher, T. M. (2009). Intsolver: An interval based toolbox for global optimization. Version 1.0.</ref> and it was used to solve some problems in the [[Hundred-dollar, Hundred-digit Challenge problems]].<ref>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]].</ref>

{{Infobox software
| name = INTLAB  (Interval Laboratory) 
| author = S.M. Rump
| developer = S.M. Rump<br/>[[Cleve Moler]]<br/>[[:ja:大石進一|Shinichi Oishi]] etc.
| programming language = [[MATLAB]]/[[GNU Octave]]
| operating system = [[Unix]], [[Microsoft Windows]], [[macOS]]
| language = [[English language|English]]
| genre = [[Validated numerics]]<br/>[[Computer-assisted proof]]<br/>[[Interval arithmetic]]<br/>[[Affine arithmetic]]<br/>[[Numerical linear algebra]]<br/>[[root-finding algorithm]]<br/>[[Numerical integration]]<br/>[[Automatic differentiation]]<br/>[[Numerical methods for ordinary differential equations]]
| website = {{URL|https://www.tuhh.de/ti3/intlab/}}
}}

==Version history==
* 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
** 12/07/2016 Version 9.1
* 05/29/2017 Version 10
** 07/24/2017 Version 10.1
** 12/15/2017 Version 10.2
* 01/07/2019 Version 11
* 03/06/2020 Version 12

==Functionality==
INTLAB can help users to solve the following mathematical/numerical problems with interval arithmetic.
{{columns-list|colwidth=22em|
* [[Numerical linear algebra]]<ref name="rump"/><ref name="moore"/><ref name="acta"/><ref name="har"/> (Not only solving matrix systems or eigenvalue problems, INTLAB can handle the [[least squares]], [[Hessian matrix]],<ref name="rump"/><ref name="acta"/> and verify the positive definiteness of a given matrix<ref>S. M. Rump: Verffication of positive definiteness, [[BIT Numerical Mathematics]], 46 (2006), 433–452.</ref>)
* [[root-finding algorithm]]<ref name="rump"/><ref name="acta"/><ref name="har"/>
* [[Affine arithmetic]]<ref name="rump"/><ref>S.M. Rump, M. Kashiwagi: Implementation and improvements of affine arithmetic, Nonlinear Theory and Its Applications (NOLTA), IEICE, 2015.</ref>
* Solving ODEs rigorously (This feature includes external tools such as the '''AWA toolbox''' and the '''Taylor model toolbox''')<ref name="rump"/><ref name="acta"/><ref>Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.</ref>
* [[Automatic differentiation]]<ref name="rump"/><ref name="acta"/><ref name="har"/><ref>L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.</ref>
* [[Numerical integration]]<ref name="rump"/><ref name="acta"/>
* [[Fast Fourier transform]]<ref name="rump"/>
* Rigorously compute the [[gamma function]]<ref>S.M. Rump. Verified sharp bounds for the real gamma function over the entire floating-point range. Nonlinear Theory and Its Applications (NOLTA), IEICE, Vol.E5-N, No. 3, July, 2014.</ref>
}}
==Works cited by INTLAB==
INTLAB is based on the previous studies of the main author, including his works with co-authors.
{{columns-list|colwidth=22em|
* 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.&nbsp;1503–1512, 1996.
}}
==External links==
{{columns-list|colwidth=22em|
*[https://www.tuhh.de/ti3/intlab/ INTLAB]
*[https://www.tuhh.de/ti3/intlab/colleagues.html List of INTLAB contributors]
*[http://uivtx.cs.cas.cz/~rohn/matlab/ VERSOFT]
*[https://www.swmath.org/software/8787 INTSOLVER]
*[https://www.tuhh.de/ti3/intlab/demos/html/dawa.html Short demonstration of the AWA toolbox]
*[https://www.tuhh.de/ti3/intlab/demos/html/dtaylormodel.html Short demonstration of the Taylor model toolbox]
}}
==See also==
* [[List of numerical analysis software]]
* [[Comparison of linear algebra libraries]]

==References==
{{reflist}}

[[Category:Numerical analysis]]
[[Category:Numerical software]]
[[Category:Computational science]]
[[Category:Computer arithmetic]]