| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 96 === This paper mainly searches that provides the model of the function graph, describes with Bernstein polynomial, and promotes from a dimension to the n dimension.
The structure of this paper as follow. The first section introduces Bernstein polynomial correlation background.
The second section explains the shape of function graph
and Bernstein polynomial coefficient relations. Proposition 1 provides sufficiency of Bernstein polynomial geometry character. Proposition 2 describes the continuous function geometry character by Bernstein polynomial viewpoint. The third section uses the probability method showed the high dimension Bernstein polynomial approximation theo-
rem. The fourth section explains the function uniform convergence theory with the analysis method. The fifth section explains the shape of function graph and the high dimension Bernstein polynomial coefficient relations. Discusses the coefficient take two variables as the example in certain condition limit minor function graphs change situations, may use to describe in the curved surface
geometry shape, applies in curved surface regression analysisestimate. The sixth section is a discussion. After this paper regarding how to describe the continuous function graph uses Bernstein polynomial, roughly has the system method, also has the quite good description method to the curved surface graph, has the greatest help to the curved
surface graph estimate.
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