Research On The Inverse Of Special Toeplitz Matrices And Quasi-Toeplitz Matrices

In this thesis, we mainly analyse the problem of determinant, inverse matrix and the stability of seven kinds of structure matrices （skew-symmetric Toeplitz matrices involving famous numbers, column upper-plus-lower Toeplitz matrix and column upper-plus-lower Hankel matrix, column upper-minus-lower Toeplitz matrix and column upper-minus-lower Hankel matrix, column upper-plus-rlower Toeplitz matrix and column upper-plus-rlower Hankel matrix）, and the main contents of the thesis consist of six chapters:The first chapter includes three parts, in the first part, we introduce applicd background and the current research situation of structure matrices such as circulant matrix, Toeplitz matrix in the domestic and overseas. In the second part, we give definitions of seven kinds of structure matrices and an important lemma, which are closely related to the following research. In the third part, the work of this thesis is briefly introduced.In the second chapter, skew-symmetric Toeplitz matrices involving famous numbers are considered. There are three parts in this chapter. In the first part, determinant and inverse of Fibonacci skew symmetric Toeplitz matrix are given by constructing the special transformation matrices. In the next part, determinant and inverse of Lucas skew symmet-ric Toeplitz matrix are given by constructing the corresponding transformation matrices.Finally, an example is provided to verify the effectiveness of the theorem.In chapters three, four and love, we focus on the inverses of column upper-plus-lower Toepitz matrix （TCUPL）and column upper-plus-lower Hankel matrix（HCUPL）, column upper-minus-lower Toeplitz matrix(T_CUML)and column upper-minus-lower Hankel matrix(H_CUML),column upper-plus-rlower Toeplitz matrix (T_CUPrL)and column upper-plus-rlower Hankel matrix (H_CUPrL)And the algorithms of the inverse matrices are given and the sta-bility of the inverse formulas of the new structure matrices are discussed. Then, in the fifth chapter, an example is provided to verify the feasibility of the theorem.In the last chapter, we summarize the main work of the thesis, and give some suggestions and expectations to the research in future.