INTLAB

INTLAB (Interval Laboratory)
作者	S.M. Rump; en:Cleve Moler; 大石進一など
最新版	Version 12 / 2020年3月6日 (4年前)
プログラミング; 言語	MATLAB/GNU Octave
対応OS	Unix, Microsoft Windows, macOS
対応言語	英語
サポート状況	継続中
種別	精度保証付き数値計算; 計算機援用証明; 区間演算; アフィン演算; 数値線形代数; 最適化問題; 求根アルゴリズム; 数値積分; 自動微分; 常微分方程式の数値解法
公式サイト	www.tuhh.de/ti3/intlab/
	テンプレートを表示

INTLAB (Interval Laboratory) はS.M. RumpがMATLAB/GNU Octaveで開発した区間演算ライブラリである^[1]^[2]^[3]^[4]^[5]。Windows、Linux、macOSに対応している。

バージョン履歴

12/30/1998 公開
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 (このバージョンから有償になる)
- 06/24/2013 Version 7.1
05/10/2014 Version 8
01/22/2015 Version 9 (このバージョンからGNU Octaveに対応)
- 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

主な機能

数値線形代数
- 連立方程式・固有値問題の求解と最小二乗法^[1]^[2]^[3]^[4]^[5]
- 正定値対称性の判定^[6]
- ヘッセ行列^[1]^[2]^[4]
- 勾配 (ベクトル解析)^[1]^[2]^[4]
求根アルゴリズム^[1]^[4]^[5]
アフィン演算 (en)^[1]^[7]
常微分方程式の数値解法 (2018年9月にリリースされた version 11 から搭載された機能で、AWA toolbox と Taylor model toolbox の二つがある)^[1]^[4]^[8]
自動微分^[1]^[2]^[4]^[5]^[9]
最適化問題^[1]^[2]^[4]
数値積分^[1]^[4]
高速フーリエ変換^[1]
ガンマ関数^[10]

主な活用事例

VERSOFT (MATLABで開発されたライブラリ)^[11]
INTSOLVER (大域最適化問題を解くためのライブラリ)^[12]
SIAM 10 $\times$ 10-digit challenge の求解^[2]^[13]

INTLABが引用している主な文献

INTLABが引用している主な文献一覧はContents.mに掲載されている。

S.M. Rump: Fast and Parallel Interval Arithmetic, en:BIT Numerical Mathematics 39(3), 539-560, 1999.
S. Oishi, S.M. Rump: Fast verification of solutions of matrix equations, en:Numerische Mathametik 90, 755-773, 2002.
T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product, en: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, en: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. en: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. en:SIAM Journal on Scientific Computing (SISC), 31(2):1269-1302, 2008.
S.M. Rump: Ultimately Fast Accurate Summation, en: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. en:Journal of Computational and Applied Mathematics (JCAM), 242:185-212, 2013.
S.M. Rump. Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. en: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, en:SIAM Journal of Numerical Analysis 22, 604-616 (1985)
S.M. Rump: Expansion and Estimation of the Range of Nonlinear Functions, en:Mathematics of Computation 65(216), pp. 1503-1512, 1996.

開発協力者

出典

[脚注の使い方]

^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k 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 ^d ^e ^f ^g 大石進一、荻田武史、柏木雅英ほか『精度保証付き数値計算の基礎』コロナ社、2018年。ISBN 9784339028874。国立国会図書館書誌ID:029048299。
^ ^a ^b Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. SIAM.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. en:Acta Numerica, 19, 287-449.
^ ^a ^b ^c ^d Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).
^ Rump, Siegfried M (2006). “Verification of positive definiteness”. BIT Numerical Mathematics (Springer) 46: 433-452. doi:10.1007/s10543-006-0056-1.
^ Rump, Siegfried M; Kashiwagi, Masahide (2015). “Implementation and improvements of affine arithmetic”. Nonlinear Theory and Its Applications, IEICE (The Institute of Electronics, Information and Communication Engineers) 6 (3): 341-359. doi:10.1587/nolta.6.341. https://doi.org/10.1587/nolta.6.341.
^ LOHNER R. J. (1987). “Enclosing the Solutions of Ordinary Initial and Boundary Value Problems”. Computer Arithmetic, Scientific Computation and Programming Languages (B. G. Teubner): 225-286. CRID 1572261550533637504.
^ L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.
^ Rump, Siegfried M (2014). “Verified sharp bounds for the real gamma function over the entire floating-point range”. Nonlinear Theory and Its Applications, IEICE (The Institute of Electronics, Information and Communication Engineers) 5 (3): 339-348. doi:10.1587/nolta.5.339. https://doi.org/10.1587/nolta.5.339.
^ 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. SIAM.

外部リンク

[rump-1] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k S.M. Rump: INTLAB - INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77-104. Kluwer Academic Publishers, Dordrecht, 1999.

[oishi-2] ^ ^a ^b ^c ^d ^e ^f ^g 大石進一、荻田武史、柏木雅英ほか『精度保証付き数値計算の基礎』コロナ社、2018年。ISBN 9784339028874。国立国会図書館書誌ID:029048299。

[moore-3] Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. SIAM.

[acta-4] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. en:Acta Numerica, 19, 287-449.

[har-5] Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).

[6] Rump, Siegfried M (2006). “Verification of positive definiteness”. BIT Numerical Mathematics (Springer) 46: 433-452. doi:10.1007/s10543-006-0056-1.

[7] Rump, Siegfried M; Kashiwagi, Masahide (2015). “Implementation and improvements of affine arithmetic”. Nonlinear Theory and Its Applications, IEICE (The Institute of Electronics, Information and Communication Engineers) 6 (3): 341-359. doi:10.1587/nolta.6.341. https://doi.org/10.1587/nolta.6.341.

[8] LOHNER R. J. (1987). “Enclosing the Solutions of Ordinary Initial and Boundary Value Problems”. Computer Arithmetic, Scientific Computation and Programming Languages (B. G. Teubner): 225-286. CRID 1572261550533637504.

[9] L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.

[10] Rump, Siegfried M (2014). “Verified sharp bounds for the real gamma function over the entire floating-point range”. Nonlinear Theory and Its Applications, IEICE (The Institute of Electronics, Information and Communication Engineers) 5 (3): 339-348. doi:10.1587/nolta.5.339. https://doi.org/10.1587/nolta.5.339.

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

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

[13] Bornemann, F., Laurie, D., & Wagon, S. (2004). The SIAM 100-digit challenge: a study in high-accuracy numerical computing. SIAM.

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INTLAB

バージョン履歴

主な機能

主な活用事例

INTLABが引用している主な文献

開発協力者

出典

関連項目

関連文献

ドイツ語

日本語

外部リンク