Based On The The Displacement Right Block Toeplitz Matrix Inverse

Structure matrix is a kinds of matrices which is encountered usually. such as cyclic matrix, Toeplitz, Hankel, Frobenius, Sylvester, Subresultant, Bezout, Vandermonde, Cauchy, Loewner and Pick matrices are often appear in algebraic and numerical computing, especially in engineering, Communication and statistics. These structure matrices have relations with different practical application.Because of the structure matrix playing an important role in practical applications , so it is particularly necessary to make a researching about it. There are many scholars in international and domestic are engaged in this field. In view of the characteristics of the structure matrix, some fast algorithms have been produced, such as fast Fourier transform ( FFT), and some fast algorithms which are derived from the fast Fourier transform. In addition,the displacement structure of a structure matrix will be available by implementing the displacement transform for the structure matrix,as a result of that a lot of fast algorithms are appering.And some methods of getting the inversion of a structure matrix are generating through its displacement structure. For example, the representation of a Toeplitz matrix's inversion.In this paper, the main using the block displacement operator get some algorithms which are for getting the inversion of a block Toeplitz matrix .And the inverse matrix can be expressed by the sum of some block circulant matrix .The main contents are as follows:First,we introduce the introduction and the background and the current situation and development trend of the future.Second, we introduce the basic concept and some nature of displacement, as well as some conclusions related and simple application.Third, by using some conclusions of the displacement and block circulant matrices, we get the explicit represetation of a block Toeplitz matrix's inversion, and the summary of this chapter.