A fast polygon inflation algorithm to compute the area of feasible solutions for three‐component systems. II: Theoretical foundation, inverse polygon inflation, and FAC‐PACK implementation
A fast polygon inflation algorithm to compute the area of feasible solutions for three‐component systems. II: Theoretical foundation, inverse polygon inflation, and FAC‐PACK implementation
复制标题
一种计算三分量系统可行解面积的快速多边形膨胀算法II：理论基础、逆多边形膨胀和FAC-PACK实现。
DOI：
10.1002/cem.2612
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发表时间：
2014
影响因子：
2.4
通讯作者：
K. Neymeyr
中科院分区：
文献类型：
--
作者：
M. Sawall;K. Neymeyr
多元曲线分解方法的可行解区域（AFS）是给定约束条件下可行解的连续体。本文仅在非负解的条件下计算AFS。这项工作是关于AFS计算的多边形膨胀算法的论文（J. Chemometrics 28：106-116，2013）的延续。在第二部分中，分析了AFS的各种特性。首先证明了它的有界性，这是数值计算的必要条件。其次，它表明，起源是从来没有包含在该地区的可行解。这一事实是反多边形膨胀算法的基础，该算法允许计算包含孔的AFS的特定类型。
The area of feasible solutions (AFS) of a multivariate curve resolution method is the continuum of feasible solutions under the given constraints. In the current paper, the AFS is computed only on the condition of nonnegative solutions. This work is a continuation of a paper (J. Chemometrics 28:106–116, 2013) on the polygon inflation algorithm for AFS computations. In this second part, various properties of the AFS are analyzed. First, its boundedness is proved, which is a necessary condition for its numerical computation. Second, it is shown that the origin is never contained in the area of feasible solutions. This fact is the basis for the inverse polygon inflation algorithm, which allows to compute specific types of an AFS containing a hole.