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Formal solution of an interval system of linear equations with an application in static responses of structures with interval forces

机译：线性方程组区间系统的形式化解及其在带力结构的静力响应中的应用

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摘要

We are concerned with the so called formal solution of an interval system of linear equations. We focus on the case where the coefficient matrix is deterministic (real) and the right-hand side is an interval vector. We show that the set of formal solutions represents a convex polyhedral set. We propose new properties of the formal solution related to its existence, uniqueness and robustness. As particular classes of problems we investigate also the situation where the coefficient matrix is an M-matrix or H-matrix. Example problems related to the structures, such as 6-bar truss and a rectangular sheet, are solved to illustrate the computational aspects of the methods.
机译：我们关注线性方程的区间系统的所谓形式解。我们关注系数矩阵是确定性（实数）且右侧是间隔向量的情况。我们证明形式解的集合代表凸多面体集合。我们提出了形式化解决方案的新属性，涉及它的存在，唯一性和鲁棒性。作为特定类别的问题，我们还研究系数矩阵是M矩阵还是H矩阵的情况。解决了与结构相关的示例问题，例如6杆式桁架和矩形板，以说明该方法的计算方面。

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  • 来源
    《Applied Mathematical Modelling》 |2017年第10期|105-117|共13页
  • 作者

    S. Chakraverty; M. Hladik; D. Behera;

  • 作者单位

    Department of Mathematics, National Institute of Technology Rourkela, 769008, Odisha, India;

    Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranski nam. 25, Prague 118 00, Czechia;

    Department of Mathematics, National Institute of Technology Rourkela, 769008, Odisha, India;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Interval system of linear equations; Interval number; Truss; Rectangular sheet;

    机译：线性方程的区间系统;间隔号;桁架;矩形板;

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