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线性方程组求解计算涉及到航空航天、计算机计算程序、环境科学、会计统计计算、隐身器件设计等国民经济与国防建设等方面,其中往往需要求解一个或一系列大型线性系统。反问题就是所谓的已知有一组复数,之后要求构造一个矩阵A,使其具有某种性质,并且求得的矩阵A的特征值也恰好是我们之前知道的那组复数。而且,随着问题规模所需的计算量增加,相应线性系统的未知数个数也在增加,有的上百万或千万,更有甚者竟达到上亿。在本文中,我们通过与线性方程组的反问题相关的两组例题,了解了每到例题的解题方法,以及该问题涉及到的对于线性方程组反问题在经济中的应用,还有一些相关的推论定理证明以及应用。
The calculation of linear equations involves the national economy and national defense construction of aerospace, computer programs, environmental sciences, accounting and computing, and stealth device design. Often it is necessary to solve one or a series of large linear systems. The inverse problem is what is known as a set of complex numbers, which is followed by the construction of a matrix A that has some property and the eigenvalues of the matrix A that we have obtained are exactly the same set of complex numbers we know before. Moreover, as the amount of computation required for the scale of the problem increases, the number of unknowns in the corresponding linear system is also increasing, some or tens of millions, or even more than 100 million. In this paper, we use two sets of examples related to the inverse problems of linear equations to find out how to solve each problem, and what the problem involves in the economic application of the inverse problems of linear equations. In addition, some Related corollary theorem proving and application.