{"title":"An improved two-step method for inverse singular value problems","authors":"Wei Ma","doi":"10.21136/AM.2026.0096-25","DOIUrl":null,"url":null,"abstract":"<div><p>Based on the technique of T. Ogita and K. Aishima (2020) and J. A. Ezquerro and M. A. Hernández (2012), we designed an improved two-step method for solving the inverse singular value problems. Compared with other existing two-step methods, the proposed method has comparable computational cost. However, computing the product of matrices is simpler than solving linear equations and has no instability problem caused by ill-conditioning in solving linear equations, and thus it seems more stable and greatly reducing computational costs. Under appropriate assumptions, the proposed method is proved to be convergent with the cubic root-convergence rate. The proposed method is applied to the noise reduction for modal parameters estimation and indicates that it can significantly remove noise from measured signals and accurately estimate the modal frequencies and damping ratios. The numerical results demonstrate the effectiveness of the improved method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"71 1","pages":"59 - 88"},"PeriodicalIF":0.6000,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2026.0096-25","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Based on the technique of T. Ogita and K. Aishima (2020) and J. A. Ezquerro and M. A. Hernández (2012), we designed an improved two-step method for solving the inverse singular value problems. Compared with other existing two-step methods, the proposed method has comparable computational cost. However, computing the product of matrices is simpler than solving linear equations and has no instability problem caused by ill-conditioning in solving linear equations, and thus it seems more stable and greatly reducing computational costs. Under appropriate assumptions, the proposed method is proved to be convergent with the cubic root-convergence rate. The proposed method is applied to the noise reduction for modal parameters estimation and indicates that it can significantly remove noise from measured signals and accurately estimate the modal frequencies and damping ratios. The numerical results demonstrate the effectiveness of the improved method.
基于T. Ogita和K. aiishima（2020）和J. A. Ezquerro和M. A. Hernández（2012）的技术，我们设计了一种改进的两步法求解逆奇异值问题。与现有的两步法相比，该方法具有相当的计算成本。然而，计算矩阵的乘积比求解线性方程简单，并且不存在求解线性方程时因条件不良而产生的不稳定性问题，因此显得更加稳定，大大降低了计算成本。在适当的假设条件下，证明了该方法具有三次根收敛率。将该方法应用于模态参数估计的降噪，结果表明，该方法能有效地去除实测信号中的噪声，准确地估计出模态频率和阻尼比。数值结果表明了改进方法的有效性。
期刊介绍：
Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering.
The main topics covered include:
- Mechanics of Solids;
- Fluid Mechanics;
- Electrical Engineering;
- Solutions of Differential and Integral Equations;
- Mathematical Physics;
- Optimization;
- Probability
Mathematical Statistics.
The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.
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