11.8 KB · ⇊ 7 parts · ⤓ Micron 11.8 KB · ⤓ HTML 25.3 KB

top

INTLAB (INTerval LABoratory) is an interval arithmetic librarycite-ref-rump-1-0[1]cite-ref-moore-2-0[2]cite-ref-acta-3-0[3]cite-ref-har-4-0[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 VERSOFTcite-ref-5[5] and INTSOLVER,cite-ref-6[6] and it was used to solve some problems in the Hundred-dollar, Hundred-digit Challenge problems.cite-ref-7[7]

• Version history

• Functionality

• Works cited by INTLAB

• External links

• See also

• References

• 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

INTLAB can help users to solve the following mathematical/numerical problems with interval arithmetic.

• Numerical linear algebracite-ref-rump-1-1[1]cite-ref-moore-2-1[2]cite-ref-acta-3-1[3]cite-ref-har-4-1[4] (Not only solving matrix systems or eigenvalue problems, INTLAB can handle the least squares, Hessian matrix,cite-ref-rump-1-2[1]cite-ref-acta-3-2[3] and verify the positive definiteness of a given matrixcite-ref-8[8])

• root-finding algorithmcite-ref-rump-1-3[1]cite-ref-acta-3-3[3]cite-ref-har-4-2[4]

• Affine arithmeticcite-ref-rump-1-4[1]cite-ref-9[9]

• Solving ODEs rigorously (This feature includes external tools such as the AWA toolbox and the Taylor model toolbox)cite-ref-rump-1-5[1]cite-ref-acta-3-4[3]cite-ref-10[10]

• Automatic differentiationcite-ref-rump-1-6[1]cite-ref-acta-3-5[3]cite-ref-har-4-3[4]cite-ref-11[11]

• Numerical integrationcite-ref-rump-1-7[1]cite-ref-acta-3-6[3]

• Fast Fourier transformcite-ref-rump-1-8[1]

• Rigorously compute the gamma functioncite-ref-12[12]

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.

• INTLAB

• List of INTLAB contributors

• VERSOFT

• INTSOLVER

• Short demonstration of the AWA toolbox

• Short demonstration of the Taylor model toolbox

• List of numerical analysis software

• Comparison of linear algebra libraries

cite-note-rump-11. ↑ S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.

cite-note-moore-22. ↑ Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics.

cite-note-acta-33. ↑ Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287–449.

cite-note-har-44. ↑ Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).

cite-note-55. ↑ Rohn, J. (2009). VERSOFT: verification software in MATLAB/INTLAB.

cite-note-66. ↑ Montanher, T. M. (2009). Intsolver: An interval based toolbox for global optimization. Version 1.0.

cite-note-77. ↑ 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.

cite-note-88. ↑ S. M. Rump: Verffication of positive definiteness, BIT Numerical Mathematics, 46 (2006), 433–452.

cite-note-99. ↑ S.M. Rump, M. Kashiwagi: Implementation and improvements of affine arithmetic, Nonlinear Theory and Its Applications (NOLTA), IEICE, 2015.

cite-note-1010. ↑ Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.

cite-note-1111. ↑ L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.

cite-note-1212. ↑ 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.