アフィン演算

数値解析・精度保証付き数値計算においてアフィン演算（アフィンえんざん、英: affine arithmetic）は区間演算における区間幅の増大を抑止するために作られた演算方式である。 須永照雄や R. Mooreによって開発された区間演算は現代では精度保証付き数値計算を含む様々な分野に応用されているが、計算を繰り返すと区間幅が増大してしまい、有意義な結果が得られなくなるという致命的な弱点があった (これが区間演算・精度保証付き数値計算の普及を妨げる一因となっている)。そこで多くの技術者・研究者たちがこの難点を克服すべく研究を積み重ねてきた。アフィン演算はその成果物の一つである。 アフィン演算はMATLAB/GNU Octaveで作られた区間演算ライブラリINTLABに搭載されている他、 常微分方程式の数値解法 求根アルゴリズム 最適化問題 混合信号 (英: mixed signal systems) 電力潮流 (英: power flow) 電気回路または電子回路 にも活用されている。 アフィン演算をよりよくしようという研究もおこなわれており、これらの手法は拡張アフィン演算 (英: extended affine arithmetic)、または変形アフィン演算 (英: modified affine arithmetic)などと総称される。 INTLAB kv - GitHub (C++によるライブラリ) Libaffa (C++によるライブラリ) libaffa - GitHub YalAA (C++によるライブラリ) yalaa - GitHub ASOL asol - GitHub [脚注の使い方] ^ a b c d 『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。 ^ T. Sunaga, Theory of interval algebra and its application to numerical analysis. (1958). RAAG memoirs, 29–46. ^ Interval Analysis. Englewood Cliff, New Jersey, USA: Prentice-Hall. (1966). ISBN 0-13-476853-1. ^ Moore, R. E. (1979). 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