帰納的関数を用いた数値計算の基礎的理論 : 代数系の構造と計算可能性

概要

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It is mentioned the algorithm which is necessary to solve the problem of the algebraric system on the ideal computer in this paper. If the problem is able to be solved with the recursive function, then the algorithm for that problem exists on the ideal computer, and that problem is defined as the computable one. As one of the feautures of this paper, it is shown that the computability of the problem is able to be defined by the algolithm of the Horne's method which is to represent the rational number as the g-scale of notation or the continuous function as the polynominal approximation. The matter mentioned above is the essence of this paper, I show it divided by four steps as follows : (i) The first step is to derive the computability of the numbers from the algebraric system. (ii) The second step ; to define the ideal computer by above (i). (iii) The third step ; to define the computability of the function by above (i) and (ii). (iv) The final step ; to define the computability structure of the Banach space which is the expansion of above (iii) to the functional analysis.
2001-07-23