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It is well known that many problems in engineering computation and practical application are the problem of matrix calculus in nature.As we all know,there are many issues in engineering computation and practical application that ultimately boil down to a matrix computation.And different applications will lead to some of the special sparse structure of the matrix computation.In the process of dealing with the sparse matrix structure of the matrix computation(for example,eigenvalue calculation,solving linear equations,and so on), if the matrix is small,usually the classic method is feasible(for example,LU decomposition,QR algorithm,etc.).However,in many practical applications,the matrices are large and sparser,or a system of linear equations need to calculate several times until to get a satisfactory result(for example,when iteration),which will get the large loss of real significance because of the cost of the classic algorithms.As a result,to design the rapid and stable numerical algorithm by making use of some of their structure according to these sparse matrix structure features will be of great significance.Some researchers proposed an effective way to solve real symmetric tridiagonal cycle of linear equations,the article introduces a new stable and effective way to solve real symmetric pentadiagonal circulant of linear equations.Our method apply the LU decomposition,and its computing complexity is 0(n).The method has more advantages in the cost of calculating and storage than Gauss elimination.Theory and numerical experiments show that our algorithm is effective.In the first chapter,we briefly introduced the research significance to solve real symmetric pentadiagonal circulant of linear equations,structure of the article,as well as the lemma of the article.In the second chapter,we explore with the three parameters of linear equations of the solution,and analyze the different situations.In the third chapter,we use the results of the second chapter and the Woodbury formula to put forward the way of solving five TOEPLITZ angle symmetric linear equations.In the forth Chapter,we proposed a way to solve the pentadiagonal circulant symmetry of linear equations by using the lemma Woodbury formula.In the fifth Chapter,through using the optimal LU decomposition,numerical experiments show that this is an effective and stable algorithm.Compared with other methods,our method of solution in the circulation system of linear equations has a larger advantage.
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