• 论文 •

### 三行H-B插值关联矩阵的正则性

1. 华东石油学院
• 出版日期:1983-04-14 发布日期:1983-04-14

### REGULARITY OF THE THREE--ROW INCIDENCE MATRIX OF H-B INTERPOLATION PROBLEM

1. Huang Chao-fan
• Online:1983-04-14 Published:1983-04-14
1. 引言和引理Hermite-Birkhoff插值是G.D.·Birkhoff于1906年提出的,1966年I.J.Schoenberg 引出了关联矩阵的概念后有了迅速的发展.关于它的发展概况在[9—12,15]中有详尽的论述.由于引入行的结合(coalesence)方法后,可把多于三行的H-B插值关联
In this paper we suppose that the three row incidence matrix E satisfies Polya condition.Let p, r be positive integers and let the number of non--zero entries in the first and thirdrows of E be p, r respectively. Let i_1 < i_2 < … < i_p and k_1 < k_2 < … < k_r denote thepositions of the 1's in the first and third rows respectively, and let l_1 < l_2 < … < l_(p+r).denote the positions of the o's in the middle row. Suppose further that l_(s1),…,l_(sp) denote theminimal sequence with l_(sj)≥i_j, j = 1, …, p in {l_1,…, l_(p+r)}, and that {l_(s'_1),…,l_(s'_r)} = {l_1,…, l_(p+r)}\{l_(s_1),…,l_(s_p)}. Similarly suppose that l_(t'_1),…l_(t'_r) denote the minimalsequence with l_(t'_j)≥k_j, j = 1,…, r and that {l_(t_1),…, l_(t_p)} = {l_1,…, l_(p+r)}\{l_(t'_1),…, l_(t'_r)}. We shall prove the following theorem: Theorem 1. If E satisfies Polya condition and ifthen E is strong non--poised. Conjecturc. Let E = (e_(ij)) be a three--row incidence matrix with where 0 ≤ k_1 < k_2 <…< k_(2p) ≤ n. Then E is poised, if and only if k_(2p)--k_1≡1, k_(2p-1) -- k-2 ≡1, …, k_(p+1) -- k_p ≡ 1(mod 2).
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