| 摘要 |
A mathematical relation identification apparatus adapted to output a mathematical relation established among basic variables x1, ..., xp when a plurality of sets d(i) of input data, each set differentiated by an input data designation parameter i comprising p basic variables x1, ..., xp, are inputted. The principle of this invention is that, when input data are converted into q-dimensional data by 9 base functions f1, ..., fq and when vectors having the converted values as vector components form a plane, the mathematical relation as a linear combination of these base functions is established. The sets f1, ..., fq of base functions, the functions of basic variables are defined in advance. A set F(i)=(Fli, ..., Fqi) of values of base functions corresponding to the input data d(i) is determined. F(i) is assumed to be a point in q-dimensional space. From the cofactor of a determinant from the points, the mapping plane in which the square sum of the lengths of the perpendiculars from these points is the smallest is determined as the solution of an eigenvalue problem period. When the direction cosine of this plane is L1, ..., Lq, the mathematical relation (I) is outputted. This invention can be used for the interpolation of data, and the identification of an orbit and a shape.
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