类似三对角矩阵行列式的递推公式算法
A Recursive Formula Algorithm of Similar to a Tridiagonal Matrix Determinant
DOI: 10.12677/PM.2022.1211200, PDF,    科研立项经费支持
作者: 左陈宇, 代慧慧, 李梦玟, 张雨婷, 袁之成, 董 兵, 王 文:合肥师范学院数学与统计学院,安徽 合肥
关键词: 三对角行列式迭代递推Tridiagonal Determinant Iteration Recursion
摘要: 本文研究了一类特殊的类似三对角的行列式的递推公式。通过迭代关系算法表示,得到一个简洁的递推结果表示,方便在其它领域的应用。
Abstract: In this paper, we study the recurrence formula of a special kind of determinant similar to tridiagonal. A concise recursive result representation is obtained by using iterative relation algo-rithm, which is convenient for application in other fields.
文章引用:左陈宇, 代慧慧, 李梦玟, 张雨婷, 袁之成, 董兵, 王文. 类似三对角矩阵行列式的递推公式算法[J]. 理论数学, 2022, 12(11): 1869-1874. https://doi.org/10.12677/PM.2022.1211200

参考文献

[1] 北京大学数学系. 高等代数[M]. 北京: 高等教育出版社, 2019.
[2] 杨胜良. 三对角行列式及其应用[J]. 工科数学, 2002(2): 106-108.
[3] Kılıç, E. (2008) Explicit Formula for the Inverse of a Tridiagonal Matrix by Backward Continued Fractions. Applied Mathematics and Computation, 197, 345-357. [Google Scholar] [CrossRef
[4] Barrett, W.W. (1979) A Theorem on Inverses of Tridiagonal Ma-trices. Linear Algebra and Its Applications, 27, 211-217. [Google Scholar] [CrossRef
[5] Qi, F., Wang, W., Guo, B.-N. and Lim, D. (2021) Several Explicit and Recurrent Formulas for Determinants of Tridiagonal Matrices via Generalized Continued Fractions. In: Hammouch, Z., Dutta, H., Melliani, S. and Ruzhansky, M., Eds., Nonlinear Analysis: Problems, Applications and Computational Methods, Lecture Notes in Networks and Systems, Springer, Cham, Vol. 168, 233-248. [Google Scholar] [CrossRef