论文标题
足够的条件适用于线性代数方程构件的过度确定间隔系统的连接解决方案仅适用于一个矫正
Sufficient Conditions for the Joined Set of Solutions of the Overdetermined Interval System of Linear Algebraic Equations Membership to Only One Orthant
论文作者
论文摘要
根据与间隔不确定性的数据构造线性模型的构建中，考虑线性代数方程（ISLAE）的间隔系统。提出了足够的条件，即ISLAE的可允许域（AD）及其仅属于$ n $维空间的一个矫正域的足够条件，可以通过计算线性代数的方法在多项式时间内验证。在这种情况下，AD ISLAE被证明是一个凸有界的多面体，完全位于相应的正装置中。 AD ISLAE的这些特性首先允许通过线性编程方法在多项式时间内找到相应的ISLAE的解（而在通用形式的ISLAE中找到解决方案是NP-固定的问题）。其次，通过求解相应的islae获得的线性模型的系数具有线性模型系数的显着性特性的类似物，因为线性模型的系数不会在AD限制内更改其符号。提供了相应定理的公式和证明。还研究了ISLAE任意溶液对线性代数方程的假设精确系统的正常溶液的误差估计和收敛。给出了一个说明性的数值示例。
Interval systems of linear algebraic equations (ISLAE) are considered in the context of constructing of linear models according to data with interval uncertainty. Sufficient conditions for boundedness and convexity of an admissible domain (AD) of ISLAE and its belonging to only one orthant of an $n$-dimensional space are proposed, which can be verified in polynomial time by the methods of computational linear algebra. In this case, AD ISLAE turns out to be a convex bounded polyhedron, entirely lying in the corresponding ortant. These properties of AD ISLAE allow, firstly, to find solutions to the corresponding ISLAE in polynomial time by linear programming methods (while finding a solution to ISLAE of a general form is an NP-hard problem). Secondly, the coefficients of the linear model obtained by solving the corresponding ISLAE have an analogue of the significance property of the coefficient of the linear model, since the coefficients of the linear model do not change their sign within the limits of the AD. The formulation and proof of the corresponding theorem are presented. The error estimation and convergence of an arbitrary solution of ISLAE to the normal solution of a hypothetical exact system of linear algebraic equations are also investigated. An illustrative numerical example is given.
