{"title":"PC-solutions and quasi-solutions of the interval system of linear algebraic equations","authors":"S. Noskov, A. Lakeyev","doi":"10.21638/11701/spbu10.2021.304","DOIUrl":null,"url":null,"abstract":"The problem of solving the interval system of linear algebraic equations (ISLAEs) is one of the well-known problems of interval analysis, which is currently undergoing intensive development. In general, this solution represents a set, which may be given differently, de- pending on which quantifiers are related to the elements of the left and right sides of this system. Each set of solutions of ISLAE to be determined is described by the domain of compatibility of the corresponding system of linear inequalities and, normally, one nonlinear condition of the type of complementarity. It is difficult to work with them when solving specific problems. Therefore, in the case of nonemptiness in the process of solving the problem it is recommended to find a so-called PC-solution, based on the application of the technique known in the theory of multi-criterial choice, that presumes maximization of the solving capacity of the system of inequalities. If this set is empty, it is recommended to find a quasi- solution of ISLAE. The authors compare the approach proposed for finding PC- and/or quasi-solutions to the approach proposed by S. P. Shary, which is based on the application of the recognizing functional.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"69 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21638/11701/spbu10.2021.304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
The problem of solving the interval system of linear algebraic equations (ISLAEs) is one of the well-known problems of interval analysis, which is currently undergoing intensive development. In general, this solution represents a set, which may be given differently, de- pending on which quantifiers are related to the elements of the left and right sides of this system. Each set of solutions of ISLAE to be determined is described by the domain of compatibility of the corresponding system of linear inequalities and, normally, one nonlinear condition of the type of complementarity. It is difficult to work with them when solving specific problems. Therefore, in the case of nonemptiness in the process of solving the problem it is recommended to find a so-called PC-solution, based on the application of the technique known in the theory of multi-criterial choice, that presumes maximization of the solving capacity of the system of inequalities. If this set is empty, it is recommended to find a quasi- solution of ISLAE. The authors compare the approach proposed for finding PC- and/or quasi-solutions to the approach proposed by S. P. Shary, which is based on the application of the recognizing functional.
求解线性代数方程组的区间系统问题是区间分析中众所周知的问题之一,目前正处于蓬勃发展的阶段。一般来说,这个解表示一个集合,它可以以不同的方式给出,这取决于哪个量词与这个系统的左边和右边的元素相关。待确定的ISLAE的每一组解由相应的线性不等式系统的相容域和通常的互补型非线性条件来描述。在解决具体问题时,很难与他们合作。因此,在解决问题过程中的非空性的情况下,建议根据多标准选择理论中已知的技术的应用,找到所谓的pc解决方案,该解决方案假定不等式系统的解决能力最大化。如果该集合为空,建议查找ISLAE的准解。作者比较了S. P. Shary提出的基于识别泛函应用的求PC解和/或准解的方法。
期刊介绍:
The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.