頁籤選單縮合
題名 | 直交多項式之理論及應用之研究=A Study on the Theory and the Applications of Orthogonal Polynomials |
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作者 | 黃樹藩; 朱良基; Yeh, Shu-Fan; Chu, Liang-Chi; |
期刊 | 中華農學會報 |
出版日期 | 19670300 |
卷期 | 57 民56.03 |
頁次 | 頁1-23 |
語文 | chi |
關鍵詞 | 直交多項式; |
英文摘要 | It is a fact common in nature that the relationship between two characters of living things or other phenomena is not of the straightline type. In many instances they will be found to be the polynomials. For finding the suitable degrees of polynomials to fit the data, it is recommended to use the method of orthogonal polynomials which can save us lots of time to solve many sets of normal equations. There are two parts in the study: in the first part, we study the properties and construction of orthogonal polynomials, and try to find the practical short methods of calculating the values of orthogonal polynomials when the levels of independent variables are equally or unequally spaced; in the second part, we study the methods of partition of sum of squares of orthogonal contrasts among unequally spaced levels of a treatment factor, and the construction of response equations of fertilizer experiment. From the theoretical study, we know that there are lots of ways for constructing orthogonal polynomials from the polynomial function of an independent variable, x, but the results come to the same if the values of orthogonal polynomials are integers reduced to lowest terms. There are four methods under investigation; i.e. the general method in which the values of orthogonal function are directly obtained by the constraints of Σfi(x)fj(x)=0, the method of solving a set of simultaneous equations constructed by the moments of x's, the Abbreviated Doolittle method of solving multiple regression equation of orthogonal polynomials on powers of x's, and the recursive solution presented by D.S. ROBSON. In order to present the sufficient uses of the data of an experiment, two examples of fertilizer experimental data were used to explain the construction of orthogonal comparisons of unequal levels of an experimental factor, and the construction of the response eauation of fertilizers by using the values of orthogonal polynomials. |
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