I_(01)逼近和多项式计算中的系数舍入(续)

一、I_(01)逼近的不唯一性 1]中我们证明了I_(01)逼近定理,指出:若有偶多项式P_(2n)(x)=sum from k-0 to n (a_(2k)x~(2k)),x∈-1,1],其系数满足0≤a_(2k)<1,k=0,1,…,n,则存在一个次数至多为2n且只以0和1

I_(01) APPROXIMATION AND THE ROUND-OFF PROBLEM FOR COEFFICIENTS IN COMPUTATION OF POLYNOMAILS (CONTINUED)

This paper investigates further the round-off problem for coefficients in computa-tion of polynomails based on author's previous paper1]. To do this, it discusses non-uniqueness of I_(01), approximation, gives a more precise estimate method for round-offerror, and generalizes the main result of 1] to more general interval instead of 0, 1].Finally, some examples are given to demonstrate the advantages of our round-off crite-rion: round-off error is smaller, its use is simple, and the rough estimate for round-offerror sufficient for common applications is unified -- there is no need of any com-putation in use.