Dijana Mosić, Predrag S. Stanimirović, Lev A. Kazakovtsev
{"title":"Minimization problem solvable by weighted m-weak group inverse","authors":"Dijana Mosić, Predrag S. Stanimirović, Lev A. Kazakovtsev","doi":"10.1007/s12190-024-02215-z","DOIUrl":null,"url":null,"abstract":"<p>The first point of this research is to develop several representations for the weighted <i>m</i>-weak group inverse. Secondly, we consider the minimization problem <span>\\(\\min \\Vert W(AW)^{m+1}X-(WA)^mB\\Vert _F\\)</span>, <span>\\(m\\ge 1\\)</span> in the Frobenius norm, subject to constraint <span>\\(\\mathcal{R}(X)\\subseteq \\mathcal{R}((AW)^k)\\)</span>, where the exponent <i>k</i> is defined as the maximum between indices of <i>AW</i> and <i>WA</i>. The solution is expressed in terms of weighted <i>m</i>-weak group inverse. Particular settings of obtained results recover several known results in the literature. A representation in the form of an appropriate outer inverse of <i>WAW</i> with given image and kernel is obtained.</p>","PeriodicalId":15034,"journal":{"name":"Journal of Applied Mathematics and Computing","volume":"129 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02215-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The first point of this research is to develop several representations for the weighted m-weak group inverse. Secondly, we consider the minimization problem \(\min \Vert W(AW)^{m+1}X-(WA)^mB\Vert _F\), \(m\ge 1\) in the Frobenius norm, subject to constraint \(\mathcal{R}(X)\subseteq \mathcal{R}((AW)^k)\), where the exponent k is defined as the maximum between indices of AW and WA. The solution is expressed in terms of weighted m-weak group inverse. Particular settings of obtained results recover several known results in the literature. A representation in the form of an appropriate outer inverse of WAW with given image and kernel is obtained.
这项研究的第一点是为加权 m 弱群逆建立几个表示法。其次，我们考虑最小化问题 \(\min \Vert W(AW)^{m+1}X-(WA)^mB\Vert _F\), \(m\ge 1\) in the Frobenius norm, subject to constraint \(\mathcal{R}(X)\subseteq \mathcal{R}((AW)^k)\), 其中指数 k 被定义为 AW 和 WA 的指数之间的最大值。解用加权 m 弱群逆表示。所获结果的特定设置恢复了文献中的几个已知结果。在给定图像和核的情况下，可以用适当的 WAW 外逆形式表示。
期刊介绍：
JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
