| Co-Investigator(Kenkyū-buntansha) |
HASEGAWA Takemitsu Fukui University, Faculty of Engineering Professor, 工学部, 教授 (70023314)
MITSUI Taketomo Graduate School of Human Informatics, Nagoya University Professor, 人間情報学研究科, 教授 (50027380)
SAITO Satoshi Graduate School of Engineering Nagoya University Research Assistan, 工学部, 助手 (70252252)
ZHANG Shao-Liang Institute of Information Sciences and Electronics, University of Tsukuba, Assist, 電子・情報工学系, 講師 (20252273)
SUGIURA Hiroshi Graduate School of Engineering Nagoya University Associate Professor, 工学部, 助教授 (60154465)
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| Research Abstract |
To construct user-friendly mathematical software, we studied on numerical analysis and human-interface for mathematical computation. In the field of numerical analysis, we developed new algorithms for fundamenetal computational task, i.e., algebraic equations (T.Torii & H.Sugiura with collaborators), ordinary differential equations (T.Mitsui & H.Sugiura with collaborators), Stochastic Differential Equations (T.Mitsui & H.Sugiura with collaborators), Delay-Differential Equations (by T.Mitsui with collaborators), Soliton Equations (T.Mitsui with collaborators), Numerical Integration (T.Hasegawa, T.Torii & H.Sugiura with collaborators), Linear Equations (S.-L.Zhang, T.Mitsui, T.Hasegawa, T.Torii & H.Sugiura with collaborators), polynomial remainder sequence for rational apploximation of function (T.Torii & H.Sugiura with collaborators).
In the field of human-interface for mathematical computation, we studied mathematical notation understanding (T.Torii & H.Sugiura with collaborators) and curve-surface generation (T.Torii & H.Sugiura with collaborators). On the research of the first theme, we achieved fundamental results of the input and parsing of mathematical notation for improving the environment of mathematical computation. Using our result, we can construct environment of programing with natural mathematical notations. Our result also gives a foundation for constructing a data-base which contains data written in mathematical notations, for example, a table of mathematical formulae. On the second theme, we studied generation of curve and surface with constraints, and propose several new algorithms. It is natural in real geometric design that curves or surfaces must satisfy some constraints, for example, positivity, monotonicity or convexity.
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