具有跳跃的等间距稀疏插值问题的多项式同伦方法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-03-13 DOI:10.1016/j.cam.2025.116623

Panpan Zhao , Bo Yu , Libin Jiao

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引用次数: 0

摘要

研究了具有跳变的等间距稀疏插值问题。这样的问题涉及到解一个多项式系统，它是无跳变情况下多项式系统的推广。研究了该多项式系统的一些有趣的性质。对于某些特殊情况，一般数据的孤立解的数目得到了准确估计；对于其他一些情况，提出了解的个数的猜想。然后，在系数参数同伦方法的基础上，提出了一类只需跟踪少量路径的高效算法。初步的数值试验表明，该算法是可行的。

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Polynomial homotopy methods for the equally spaced sparse interpolation problem with jump

In this paper, the equally spaced sparse interpolation problem with jump is considered. Such a problem concerns solving a polynomial system which is a generalization of that in the case without jump. Properties of this polynomial system are investigated for some interesting cases. For some special cases, the numbers of isolated solutions for generic data are accurately estimated; for some other cases, a conjecture on the numbers of solutions is proposed. And then, based on the coefficient parameter homotopy method, a class of efficient algorithms, in which only a few number of paths need to be traced, are proposed. Preliminary numerical tests show that the proposed algorithms are promising.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.