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非線形方程式求根アルゴリズムの宣言的形式言語の設計

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(1)情報処理学会論文誌. プログラミング. Vol.9 No.3 24 (June 2016). 発表概要. 非線形方程式求根アルゴリズムの宣言的形式言語の設計 嶋吉 隆夫1,a). 天野 晃2. 2016年1月13日発表. 近年,数値計算が行われる環境は,クラスタ PC や GPGPU(general-purpose computing on graphics processing units),クラウドコンピューティングなど非常に多様化している.そこで用いられる数値計算 アルゴリズムは一般的に,手続き型プログラミング言語を用いて実装されたライブラリの形態で配布,利 用される.このやり方は,計算性能の面で有利であるが,一方で,計算実行環境に対応した利用アルゴリ ズムの実装が公開されていない場合は自らアルゴリズムを移植する必要があるという,可用性および生産 性の問題がある.そこで,本発表では,非線形方程式の求根アルゴリズムを対象とした XML ベース形式 言語を提案する.この形式言語では,求根アルゴリズムは漸化式として定義され,プログラミング言語に 依存しない形式で MathML の Content Markup を用いて宣言的に記述される.この宣言的記述に含まれ る数式と数学変数との関係を解析することで,対象アルゴリズムの抽象化された計算手順を得ることがで きる.この抽象的計算手順は,具体的なプログラミング言語によるプログラムコードに変換可能である. 本手法により,多様な環境における求根アルゴリズムの実装コストを削減できると考えられる.. Design of a Declarative Formal Language for Root-finding Algorithms of Nonlinear Equations Takao Shimayoshi1,a). Akira Amano2. Presented: January 13, 2016. In recent years, numerical computations are executed using various computing environments such as PC clusters, GPGPU (general-purpose computing on graphics processing units) and cloud computing. Numerical algorithms employed in the numerical computations are generally distributed within libraries implemented in procedural programming languages such as Fortran, C, and MATLAB. This conventional manner has an advantage in computational performance, but also has a problem on availability and productivity that an algorithm has to be ported onto a target environment if any implementations of the algorithm are not available on the environment. In this presentation, a XML-based formal language for root-finding algorithms of nonlinear equations is introduced. In this formal language, a root-finding algorithm is declaratively defined as a set of mathematical recurrence formulas using Content Markup of MathML. This description is independent of any programming languages. By analyzing relationships among mathematical equations and mathematical variables in the description, an abstract calculation procedure of the described algorithm can be obtained. The abstract procedure is convertible into program codes in a concrete programming language. This scheme can reduce costs for implementation of root-finding algorithms on various environments.. 1. 2. a). 九州大学情報基盤研究開発センター Research Institute for Information Technology, Kyushu University, Fukuoka 812–8581, Japan 立命館大学生命科学部 College of Life Sciences, Ritsumeikan University, Kusatsu, Shiga 525–8577, Japan [email protected]. c 2016 Information Processing Society of Japan . 24.

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