论文成果
POLYNOMIAL HOMOTOPY METHOD FOR THE SPARSE INTERPOLATION PROBLEM PART I: EQUALLY SPACED SAMPLING
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- 论文类型：期刊论文
- 发表时间：2016-01-01
- 发表刊物：SIAM JOURNAL ON NUMERICAL ANALYSIS
- 收录刊物：SCIE、EI
- 文献类型：J
- 卷号：54
- 期号：1
- 页面范围：462-480
- ISSN号：0036-1429
- 关键字：sparse interpolation; polynomial system; homotopy method; global
convergence
- 摘要：In this paper, the solution of the polynomial system arising from sparse interpolation problems with equally spaced sampling is studied. Exploiting the special structure of the polynomial system, it is proved that all its solutions lie in one orbit for generic data. Then, based on the coefficient parameter homotopy method, an efficient algorithm for solving the system is proposed. Smoothness and accessibility of the coefficient parameter homotopy hold for the constant terms of the start system generated by a randomly chosen starting point. So, in the coefficient parameter homotopy method, it needs no computational cost in the first phase and only one path needs to be traced in the second phase. Preliminary numerical tests show that the proposed algorithm is promising.
