多变量指数多项式的稳定恢复和模型还原

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-03-01 DOI:10.1016/j.jsc.2024.102313

Juan Manuel Peña , Tomas Sauer

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引用次数: 0

摘要

多变量指数多项式的复原，即 Prony 问题的多变量版本，可以通过使用比最小需要的多整数函数样本更多的样本来稳定。我们提出了一种考虑到这些额外信息的算法，并证明了代数恢复方法 SMILE 的后向误差估计。此外，我们还给出了一种用给定结构的指数多项式序列来近似数据的方法，作为多变量模型还原方向上的一步。

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Stabilized recovery and model reduction for multivariate exponential polynomials

Recovery of multivariate exponential polynomials, i.e., the multivariate version of Prony's problem, can be stabilized by using more than the minimally needed multiinteger samples of the function. We present an algorithm that takes into account this extra information and prove a backward error estimate for the algebraic recovery method SMILE. In addition, we give a method to approximate data by an exponential polynomial sequence of a given structure as a step in the direction of multivariate model reduction.

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.