Analysis of Accuracy Decreasing in Polynomial Remainder Sequence with Floating-point Number Coefficients

概要

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Let (P_1, P_2, P_3, . . .) be the univariate polynomial remainder sequence with floating. point number coefficients. Letλ roots of P_l be close toμ roots of P_2, and let deg (P_k)=min {λ,μ}. Then, the accuracy of the coefficients of P_<k+i>, i>0, decreases significantly. The accuracy decreasing in P_<k+i> was investigated in a previous paper. This paper almost clarifies the phenomenon of accuracy decreasing in P_<k+i>, i= 1, 2, . . . , under the restriction that degrees of initial polynomials are not large. It is shown that if the close roots are concentrated at one point then the accuracy decreases at each calculation of P_<k+i>, i>O. If the close roots are distributed around r points, r>1, which are mutually well-distant then the accuracy decreases each time the degree of remainder decreases by r. Furthermore, the amount of decrease of accuracy is clarified, with emphasis on the case P_2(x)z dP_1(x)/dx.
一般社団法人情報処理学会の論文
1990-03-15