Computing Square Roots Of Generalized Centrosymmetric Matrices

The problem for solving square roots of matrices often appear in the solution of control system and the boundary value problem of differential equation. The existence of square roots of matrices is nontrivial.For a matrix, there may exit none,finite or infinite square roots.In this thesis,we consider the problem for the square roots of two classes of structured matrices,i.e.,the problem for the square roots of generalized centrosymmetric matrices and generalized centrohermitian matrices.This thesis is organized as follows:In the first chapter,we mainly introduce the background,the main contents and the originalities of the thesis.In the second chapter,we briefly review some basic definitions and notation which will be used in the thesis.In the third chapter, we discuss some properties of the square roots of nonsingular generalized centrosymmetric matrices and nonsingular generalized centrohermitian matrices.In the fourth chapter,we first review the conventional algorithms for computing the square roots of matrices.By exploiting the special structure of generalized centrosymmetric matrices and generalized centrohermitian matrices , we then propose fast algorithms,which ensure the improvement of computational speed.