| With the rapid development of the science and technology, modern science and technologyattach more and more importance and concern to matrix theory when they solvemathematic problem. And matrix theory is being used extensively in many fields such ascomputational mathematics, mechanics, control theory and so on.Determinant is important characters of matrix, many domestic and overseas scholarshave made a great of research and got several famous inequalities: Hadamard inequality,Hadamard-Fischer inequality, Oppenheim inequality and so on. The doubly diagonallydominant matrices is one special class of matrix, they have many special properties. Inthis paper, we give some new bounds of determinants of the doubly diagonally dominantmatrices.In chapter one, we first introduce some background knowledge and recent works fordoubly diagonally dominant matrices, H matrix, the Schur complements and determinants.Then we give some basic symbols and definitions used in our paper.In chapter two, we first obtain a strictly diagonally dominant matrices by doublydiagonally dominant matrices multiplying a positive diagonal matrix at right, than weobtain some new estimations of bounds for the determinants of the doubly diagonallydominant matrices by using the estimations of the determinants of the strictly diagonallydominant matrices. Finally, we explaining the results in our paper are more accurate thanthe former under certain conditions by numerical examples.In chapter three, we first obtain a strictly diagonally dominant matrices by solvingthe Schur complements of the doubly diagonally dominant matrices, than we use the estimationsof the determinants of the strictly diagonally dominant matrices and employinequalities techniques to extend some existing results. According to many numerical examples,we further explaining the results in our paper is superior to the former undercertain conditions. At the same time, we make comparisons with the two methods bynumerical examples.
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