INTLAB (INTerval LABoratory) is an interval arithmetic library[1][2][3][4] 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[5] and INTSOLVER,[6] and it was used to solve some problems in the Hundred-dollar, Hundred-digit Challenge problems.[7]
INTLAB (Interval Laboratory)Original author(s) S.M. Rump
Developer(s) S.M. Rump
Cleve Moler
Shinichi Oishi etc.
Written in MATLAB/GNU Octave
Operating system Unix, Microsoft Windows, macOS
Available in English
Type Validated numerics
Computer-assisted proof
Interval arithmetic
Affine arithmetic
Numerical linear algebra
root-finding algorithm
Numerical integration
Automatic differentiation
Numerical methods for ordinary differential equations
Website www.ti3.tu-harburg.de/rump/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
Functionality
INTLAB can help users to solve the following mathematical/numerical problems with interval arithmetic.
Numerical linear algebra[1][2][3][4] (Not only solving matrix systems or eigenvalue problems, INTLAB can handle the least squares, Hessian matrix,[1][3] and verify the positive definiteness of a given matrix[8])
root-finding algorithm[1][3][4]
Affine arithmetic[1][9]
Solving ODEs rigorously (This feature includes external tools such as the AWA toolbox and the Taylor model toolbox)[1][3][10]
Automatic differentiation[1][3][4][11]
Numerical integration[1][3]
Fast Fourier transform[1]
Rigorously compute the gamma function[12]
Works cited by INTLAB
INTLAB is based on the previous studies of the main author, including his works with 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
INTLAB
List of INTLAB contributors
VERSOFT
INTSOLVER
Short demonstration of the AWA toolbox
Short demonstration of the Taylor model toolbox
See also
List of numerical analysis software
Comparison of linear algebra libraries
References
S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.
Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics.
Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287–449.
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.
S. M. Rump: Verffication of positive definiteness, BIT Numerical Mathematics, 46 (2006), 433–452.
S.M. Rump, M. Kashiwagi: Implementation and improvements of affine arithmetic, Nonlinear Theory and Its Applications (NOLTA), IEICE, 2015.
Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.
L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.
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.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
