Promotion Of Block Circulant Matrix

Cyclic matrix class has been widely used, it is a kind of important and special matrix.Because cyclic matrix has very good properties and structure, so it is necessary to dofurther promotion and research. In this paper, for the promotion, the block circulantmatrices is studied in two types, the m heavy diagonal factor circulant matrices and the mheavy companion circulant matrices.Focus on the m heavy diagonal factor circulant matrices, this paper analyzes itsproperty, some results are obtained, and the results is given for the Euclidean algorithm forthe inverse and generalized inverse of the corresponding matrix;Focus on the m heavy companion circulant matrices, this paper mainly introduced thefast algorithm of the m heavy companion circulant linear system, give examples,and theaccuracy of the results and the main algorithm introduced is guaranteed.This thesis is divided into four chapters.In chapter1, the current research status ofcyclic matrix class is presented.In chapter2,we study the inversion algorithm of m heavydiagonal factor circulant matrices.In chapter3,we study the fast algorithm for the m heavyheavy companion circulant linear systems.In the last chapter4,the research is prospected.