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| Abstract |
The first purpose of this paper is to enunciate our general viewpoints how to formulate our stochastically approximative analysis, as we have given in this Introduction. The second purpose of this pap...er is to give each formulation to each of some fundamental problems associated with numerical analysis from the view points of the decision function approches to stochastically approximative analysis. In Part I we give two theorems concerning linear estimation formula on the basis of the non-sequental minimax procedures, which may be recognized to be preparatory to stochastically approximative analysis of more advanced and more elaborate types. In Part II we are concerned with the discussions about the uses of difference-tables in interpolatory analysis from the standpoints of stochastically approximative analysis, appealing to the frame of the WIENER space and also to successive process of statistical inferences. In Part III our emphasis lies also in the formulation of our current procedures in developing our concurrence-function in the series of given orthogonal functions and in stopping the calculation of the expansion until some adquate terms. We shall point out here as well as elsewhere the situation that some of the current procedures of numerical analysis can be formulated from the standpoints of successive process of statistical inferences after giving at least substantially their respective suitable formulation concerning the three fundamental logical schemes. Some of Part II and most of Part III are merely giving certain formulations to our problem, and it is open to further development to solve various detailed problems suggested by our formulation.show more
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