| 变系数线性递归序列收敛的充分和必要条件 |
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| 引用本文： | 陈刚.变系数线性递归序列收敛的充分和必要条件[J].南通工学院学报(自然科学版),2013(3):91-94. |
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| 作者姓名： | 陈刚 |
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| 作者单位： | 南通职业大学基础课部,江苏南通226007 |
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| 基金项目： | 江苏省高等教育教学改革研究课题重点项目（2011JSJG085） |
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| 摘 要： | 讨论由线性递归方程确定的序列的收敛性．从常系数递归序列收敛的充分必要条件出发，证明了变系数递归序列收敛的充分条件；构造反例，指出了变系数递归序列的复杂性；通过数学归纳和范数递推，给出并证明了在排除退化状态、兼顾临界状态之下，变系数递归序列收敛条件的必要性．
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| 关 键 词： | 递归序列 收敛条件 系数矩阵 特征值 |
Necessary and Sufficient Conditions for the Convergence of Linear Recurrent Sequence |
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| Authors: | CHEN Gang |
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| Institution: | CHEN Gang (Department of Basic Courses, Nantong Vocational University, Nantong 226007, China) |
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| Abstract: | The convergence of sequence determined by linear recursive equation is studied. It demonstrates a sufficiem condition for convergence of recursive sequence of variable coefficients based on the necessary and sufficient conditions in case of constant coefficients, and it points out the complexity situation of variable coefficients by constructing counter-examples. Furthermore, using mathematical induction and norm recursive, it gives the necessity of condition for convergence of sequence with variable coefficients as the exclusion of degradation state and taking into account the critical state. |
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| Keywords: | recursive sequence convergence condition coefficient matrix eigenvalue |
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