| Inengineeringscienceandtechnologyandscientificcalculation,manypracticalproblemsneed to be solved.Because it is sometimes very complex or impossible to solve the inverse of matrix directly,it is very important to find a n i terative s cheme s o t hat i t i s v ery i mportant to calculate the product of matrix and matrix when finding the inverse of m atrix.Secondly,many practical problems can be transformed into solving linear equations.Because the condition number of coefficient matrix of some linear equations is very large or close to singularity,it is very necessary to preprocess linear equations.In the introduction,the application of matrix inversion and the pretreatment of linear equations at home and abroad,as well as the main research work are introduced.The first chapter is the preparatory knowledge,which first explains the common symbols in this paper,then introduces the matrix splitting technique,conjugate gradient method and GMRES method,and finally i ntroduces the iterative schemes of Newton iterative method and Chebyshev iterative method.In the first four sections of the second c hapter,four kinds of iterative schemes of inverse matrix of approximation are given,and the selection of initial values of the above four iterative schemes is introduced in numerical cases.It is proved that proper selection of initial values can improve the operation precision and reduce the operation time of the inverse of approximation matrix.In the third chapter,the preoptimal conjugated gradient method and preprocessing GMRES method are introduced at first.Secondly,the matrices obtained by selecting the appropriate iterative steps of the four iterative schemes in chapter 2 are used as pretreatments of the preoptimal conjugated gradient method and the preconditioned GMRES method,respectively.Numerical experiments show that the above two strategies can accelerate compared with the conjugated gradient method and the GMRES method,respectively. |
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