{"title":"Submatrix constrained left and right inverse eigenvalue problem for centrosymmetric matrices","authors":"Lijun Zhao","doi":"10.1080/17415977.2020.1850716","DOIUrl":null,"url":null,"abstract":"ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix constraint, where is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) satisfying the matrix constraint, where A and are both centrosymmetric matrices. Using the similar structure of A and , we discuss the sufficient and necessary conditions for the left and right inverse eigenvalue problem having solutions, and give the expression for its general solution. Then, we discuss its optimal approximation problem and gain the expression of its solution. Last, we provide a feasible algorithm for computing the unique solution to its optimal approximation problem, which is proved by some numerical examples.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"11 1","pages":"1412 - 1428"},"PeriodicalIF":1.1000,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1850716","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems in Science and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/17415977.2020.1850716","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
ABSTRACT In this article, we will find centrosymmetric matrix solutions A of the left and right inverse eigenvalue problem under a submatrix constraint, where is also a centrosymmetric matrix. In other words, expand the system (matrix) A from the centre subsystem (submatrix) satisfying the matrix constraint, where A and are both centrosymmetric matrices. Using the similar structure of A and , we discuss the sufficient and necessary conditions for the left and right inverse eigenvalue problem having solutions, and give the expression for its general solution. Then, we discuss its optimal approximation problem and gain the expression of its solution. Last, we provide a feasible algorithm for computing the unique solution to its optimal approximation problem, which is proved by some numerical examples.
期刊介绍：
Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome.
Topics include:
-Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks).
-Material properties: determination of physical properties of media.
-Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.).
-Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.).
-Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.
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