Abstract: The calculation methods of diagonally dominant matrix in-situ replacement are researched，including the matrix determinant，the matrix equation unknown and the matrix inversion computation.Make use of the principle of matrix triangular decomposition and matrix operations fundamental to derive the calculation formula for matrix elements of simplification value，thus it further derives using of matrix elements of simplification value to compute the in-situ replacement solution formula of calculation of matrix determinant，matrix equation unknown and inverse matrix array elements.Calculation of the formula used in pure form of presentation is conducive to programming calculation，and it can realize the in-situ replacement solution according to the place of matrix elements in the matrix.The calculation space and time of this method can be saved,and the efficiency of scientific computation is improved.

Key words: diagonally dominant matrix, in-situ replacement, fast calculation