Research On Two Improved Methods For Solving Toeplitz Linear System

Toeplitz linear system is widely used in many fields such as mathematics,physics,scientific computing and information theory,and has attracted the attention of many scholars.Therefore,how to solve Toeplitz linear system quickly has become a hot research topic.At present,there are mainly two methods to solve the Toeplitz linear system:the direct method and the iterative method.Due to the higher complexity of the direct method,iterative method is often used to solve the approximate solution of Toeplitz linear system.The CSCS iterative method is the most commonly used solution.It is the first to split the Toeplitz matrix and then use two-step iteration.Based on the existing CSCS method for solving Toeplitz linear system,this paper gives two improved algorithms:The first method is a modified CSCS iterative method,which is an iterative algorithm derived from the CSCS method.The method splits the coefficient matrix of the Toeplitz linear system into the form of the difference between the circulant matrix and the reverse circulant matrix.The convergence of the method is proved theoretically.Then the number of iterations and the CPU running time of the method are analyzed by numerical experiments.The second method is to improve the double complex reference method,which is based on the existing CSCS method derived from another iterative method.In the iterative process,it iterates the iteration parameters from a single complex parameter to a double complex parameter,and proves its convergence theoretically.The numerical example is compared with the single and complex parameter CSCS method,and it runs stably under the condition of equal length and CPU runtime has been reduced.