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Ithis book we introduce current developments and applications iusing iterative methods for solving block Toeplitz systems. The block Toeplitz systems arise ia variety of applications imathematics�� scientific computing and engineering�� for instance�� image restoratioproblems iimage processing; numerical differential equations and integral equations;time series analysis and control theory. Krylov subspace methods and multigrid methods are proposed. One of the mairesults of these iterative methods is that the operatiocost of solving a large class of mx m��n��block Toeplitz systems is only required O(mn��log mn��) operations.
����This book consists of twelve chapters. Various bibliographies are placed at the end of the book. IChapter 1�� we survey some background knowledge of matrix analysis and point Toeplitz iterative solvers that will be used later to develop our block Toeplitz iterative solvers.