INTLAB

INTLAB (Interval Laboratory)
作者	S.M. Rump
開発元	S.M. Rump; en:Cleve Moler; 大石進一など
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
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.ti3.tu-harburg.de/rump/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[編集]

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)

主な機能[編集]

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[編集]

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[編集]

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[編集]

出典[編集]

[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 『精度保証付き数値計算の基礎』大石進一編著、コロナ社、2018年。
^ ^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).
^ S. M. Rump: Verffication of positive definiteness, en: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.
^ 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[編集]

[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 『精度保証付き数値計算の基礎』大石進一編著、コロナ社、2018年。

[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] S. M. Rump: Verffication of positive definiteness, en:BIT Numerical Mathematics, 46 (2006), 433-452.

[7] S.M. Rump, M. Kashiwagi: Implementation and improvements of affine arithmetic, Nonlinear Theory and Its Applications (NOLTA), IEICE, 2015.

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

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

[10] 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.

[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[編集]

主な機能[編集]

主な活用事例[編集]

INTLABが引用している主な文献[編集]

開発協力者[編集]

出典[編集]

関連項目[編集]

関連文献[編集]

ドイツ語[編集]

日本語[編集]

外部リンク[編集]