| Generalized strictly diagonally dominant matrix play an important role in matrix theory and real applications. It has numerous applications in numerical algebra,mthematical physics,cybernetics theory,electrical system theory,mathematics of economics,statistics and so on. Especially, strictly diagonally dominant periodic tridiagonal and pentadiagonal matrix play an important role in theory, and have very extensively application in numerical analysis.In this paper, we estimate the upper and lower bounds on the inverse elements of strictly diagonally dominant periodic tridiagonal and pentadiagonal matrix, improve and extend some existing results on the upper bounds of strictly diagonally dominant periodic tridiagonal matrix.In chapter one, we introduce the applied background and present conditions of research on Generalized strictly diagonally dominant matrix. Especially, emphasize the applied background and some related results on strictly diagonally dominant periodic tridiagonal and pentadiagonal matrix.In chapter two, by using the skills of the character of coefficient matrix of linear equation system be a strictly diagonally dominant periodic tridiagonal matrix and expanding and reducing inequality combine iteration idea and so on, estimating the upper and lower bounds on the inverse elements of strictly diagonally dominant periodic tridiagonal matrix, improving and extending the latest results. At the same time, by numerical examples, further illustrating the results in this paper more accurate than the latest results.In chapter three, by using the skills of the character of coefficient matrix of linear equation system be a strictly diagonally dominant pentadiagonal matrix and expanding and reducing inequality and so on, estimating the upper and lower bounds on the inverse elements of strictly diagonally dominant pentadiagonal matrix , further illustrating the accurate extend by numerical examples.
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