{"title":"Numerical methods for solving a class of matrix equations arising from inference for ranked set sampling on imperfect ranking","authors":"Qiang Niu , Binrui Shen , Yenan Wang","doi":"10.1016/j.cam.2025.116519","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate some numerical methods for a class of matrix equations with constraints arising from inference for ranked set sampling on imperfect ranking. Based on the structure of the matrix equation, two classes of numerical methods are studied to solve the problem. The first idea is to treat the problem as a simplified Riccati equation, then a Schur method and a square-root method are derived. The second idea is entirely novel, which is based on an extended Krylov subspace originated from the doubly stochastic property of the related matrices. The performance and efficiency of all the numerical solvers are verified by numerical examples.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116519"},"PeriodicalIF":2.6000,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042725000342","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/14 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate some numerical methods for a class of matrix equations with constraints arising from inference for ranked set sampling on imperfect ranking. Based on the structure of the matrix equation, two classes of numerical methods are studied to solve the problem. The first idea is to treat the problem as a simplified Riccati equation, then a Schur method and a square-root method are derived. The second idea is entirely novel, which is based on an extended Krylov subspace originated from the doubly stochastic property of the related matrices. The performance and efficiency of all the numerical solvers are verified by numerical examples.
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.
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