INTER-POLYNOMIAL DISTANCE CALCULATION DEVICE, METHOD, RECORDING MEDIUM, ONE-VARIABLE SHORTEST POLYNOMIAL CALCULATION DEVICE, METHOD, AND RECORDING MEDIUM

摘要

PROBLEM TO BE SOLVED: To obtain a distance between a polynomial f and a polynomial f=, which is closest to the polynomial f without having a duplicate zero point in a real closed section I when measured with 1∞-norm, among the polynomials having the duplicate zero points in I. SOLUTION: The smallest one of absolute values ¾t¾ is acquired, which are obtained in response to the candidates of roots in simultaneous equations, f(x)+tq(x)=0 and f'(x)+tq'(x)=0, obtained by each polynomial q(x) belonging to äΣj=1n±ej(x)} in the case of f(x)=e0(x)+Σj=1najej(x) (ajE*R), wherein E*means a symbol of sets; and ajE*R means that ajbelongs to R [Process A]. The smallest one of the absolute values ¾τ¾ is acquired, which are obtained in response to the candidates of roots in simultaneous equations, f(x)+tμeμ(x)+τpμ(x)=0, f'(x)+tμeμ'(x)+τpμ'(x)=0, obtained by each combination of an integerμbelonging to ä1, 2, ..., n} with a polynomial pμ(x) belonging to a set äΣ1≤j≤n,j≠μ±ej(x)} [Process B]. The smallest one of the values acquired in the process A and the process B is the shortest distance. COPYRIGHT: (C)2009,JPO&INPIT