About G- Circulation Loop Matrix And Matrix Solving Some Problems

Circulant matrices has been one of the most important and active research fields of the matrix theory and applied mathematic in recent years. The reasons why so many researchers devote themselves in it are mainly as follows:firstly, the circulant matrices is a kind of important special matrix, widely applied in modern technology field, such as molecular vibration, signal process, image process etc; Secondly, circulant matrices own many special and good properties and structure and has been widely applied in many fields of applied mathematic, such as control theory, optimization, matrix decomposition etc.The thesis is made up of three chapters which mainly discuss about several algorithms on how to solve the inverse matrix, multiplication of matrices of some circulant matrix. On the basis of summarizing some existed fast algorithms, I provide several new fast algorithms.Chapter one consists of the prelude and the overview of the development of circulant matrixChapter two summarizes some properties of circulant matrix, and provides the fast algorithms on multiplication and inverse of g-circulant matrices and its derivative matrices. The two fast algorithms’ computation time complexity are both O(nlog2n) as to the circulant matrix of order n. Chapter three provides a solution to the inverse of the-sum-of-the-first-and-last circulant matrix, the judgement and solution of circulant linear set under all kinds of circumstances by employing polynomial matrix theory.