本文選題：不確定變量　切入點：系數(shù)矩陣　出處：《南京理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著科學(xué)和工程技術(shù)的發(fā)展,線性代數(shù)中一般形式的線性系統(tǒng)已經(jīng)無法達到研究應(yīng)用的要求,變量為不確定的線性系統(tǒng)得到了眾人的關(guān)注。李波和朱元國教授于2014年提出了不確定線性系統(tǒng)的概念,并給出了相關(guān)求解公式。本文在此基礎(chǔ)上提出了全不確定線性系統(tǒng)(或全不確定線性方程)的概念,并定義了全不確定線性系統(tǒng)的解。隨后,文章討論了全不確定線性系統(tǒng)有解的充分條件。針對系統(tǒng)系數(shù)矩陣為方陣和非方陣的情況,本文分別給出了系統(tǒng)的求解公式以及系統(tǒng)有解的判斷條件�？紤]到求解時需要求矩陣逆,當(dāng)系數(shù)矩陣維數(shù)較大時其計算量非常大,不便于應(yīng)用,因此,本文進一步討論了關(guān)于全不確定線性系統(tǒng)的數(shù)值迭代算法求解,并分析了幾種迭代法在求解全不確定線性系統(tǒng)時其迭代格式的收斂性問題。最后,文章給出了關(guān)于全不確定線性系統(tǒng)的幾個數(shù)值例子和一個應(yīng)用實例。
[Abstract]:With the development of science and engineering technology, the general form of linear system in linear algebra has been unable to meet the requirements of research and application. In 2014, Professor Li Bo and Professor Zhu Yuanguo put forward the concept of uncertain linear system. In this paper, the concept of fully uncertain linear systems (or fully uncertain linear equations) is proposed, and the solution of fully uncertain linear systems is defined. In this paper, the sufficient conditions for the existence of solutions for fully uncertain linear systems are discussed. In this paper, the solution formulas of the system and the judgment conditions of the solution are given respectively. Considering that the inverse matrix needs to be solved, when the dimension of the coefficient matrix is large, the calculation is very large and is not easy to be applied. In this paper, we further discuss the numerical iterative algorithm for solving fully uncertain linear systems, and analyze the convergence of the iterative schemes of several iterative methods for solving fully uncertain linear systems. In this paper, several numerical examples and an application example of fully uncertain linear systems are given.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O151.2

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相關(guān)期刊論文 前1條

1 袁尚明;;非負矩陣有非負滿秋分解的條件[J];南京理工大學(xué)學(xué)報(自然科學(xué)版);1990年01期

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本文編號：1572477