Implementation and Development of Application of Fast Automatic Differentiation

快速自动微分应用的实现与开发

• 批准号: 63460131
• 负责人: IRI Masao
• 金额: $ 2.24万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-63460131/
• 关键词: Fast Automatic Differentiation; Numerical Differentiation; Rounding Error; Interval Analysis

FAST AUTOMATIC DIFFERENTIATION (FAD) was proposed by Masao IRI in 1983. The objectives of this research are to develop a software to realize FAD and its application to real-world problems and to establish FAD as a technique of numerical computation.The results of this research are as follows :(1) Improvement of FAD preprocessor : In addition to the already available FORTRAN preprocessor, an operator-overloading technique by means of c++ was developed. Those two types of implementations were improved to a software system for numerical experiment. They are capable also of computing the rounding error estimates of functions and gradients and are portable to various types of computers.(2) Rigorous theory of rounding error estimation and use of the estimation in numerical algorithms : It was theoretically proved and experimentally evidenced that, using FAD, the error estimation can be rigorous and sharper. It was pointed out how to improve the method of constructing computational graphs. Application of FAD to the solution of nonlinear equation systems and geometrical/geographical optimization problems proved the effectiveness of FAD. In fact the accuracy of the results, the computational speed, the convergence criterion, etc. Were remarkably ameliorated.(3) Hybridization of FAD and formula manipulation : This has not yet been completed because it took longer than expected for the research described in (1) and (2).The above-described research results have been publicized at research meetings at home and abroad, and turned out to lead this kind of research in the world.

快速自动微分（FAD）是由Masao IRI在1983年提出的。本研究的目的是开发一个实现FAD的软件，并将其应用于实际问题，使FAD成为一种数值计算技术，研究结果如下：（1）FAD预处理器的改进：在已有的FORTRAN预处理器的基础上，利用C++开发了一种操作符重载技术。这两种实现方式被改进为一个用于数值实验的软件系统。它们也能够计算函数和梯度的舍入误差估计，并可移植到各种类型的计算机上。(2)四舍五入误差估计的严格理论和估计在数值算法中的使用：理论证明和实验证明，使用FAD，误差估计可以是严格和尖锐的。指出了如何改进计算图的构造方法。FAD在求解非线性方程组和几何/地理优化问题中的应用证明了FAD的有效性。实际上，结果的精度，计算速度，收敛准则等显着改善。(3)FAD和公式操作的混合：由于（1）和（2）中描述的研究花费的时间比预期的长，因此尚未完成。上述研究结果已在国内外的研究会议上公布，并在世界上领先于此类研究。

项目成果

久保田 光一,伊理 正夫: "区間演算を用いた丸め誤差解析" 情報処理. 31. 1212-1219 (1990)

Koichi Kubota、Masao Iri：“使用区间运算进行舍入误差分析”信息处理 31. 1212-1219 (1990)。

IRI Masao,TSUCHIYA Takashi,HOSHI Mamoru: "Automatic Computation of Partial Derivatives and Rounding Error Estimates with Applications to Largeーscale Systems of Nonlinear Equations." Journal of Computational and Applied Mathematics. 24. 365-392 (1988)

IRI Masao、TSUCHIYA Takashi、HOSHI Mamoru：“偏导数和舍入误差估计的自动计算及其在大型非线性方程组中的应用。”计算与应用数学杂志 24. 365-392 (1988)。

室田一雄,久保田光一: 情報処理学会論文誌. 30. (1989)

Kazuo Murota、Koichi Kubota：日本信息处理学会汇刊 30。（1989 年）

Kokichi SUGIHARA and Masao IRI: "A solid modelling system free from topological inconsistency." Journal of Information Processing. 12. 380-393 (1989)

Kokichi SUGIHARA 和 Masao IRI：“一个没有拓扑不一致的实体建模系统。”

伊理 正夫,久保田 光一: "高速自動微分法" 応用数理. (1991)

Masao Iri，Koichi Kubota：“高速自动微分法”应用数学（1991）。