关键词: 海洋数据同化, 集合最优插值（EnOI）, 矩阵求逆, 矩阵分解, Choleskey分解

Abstract: In the field of ocean data assimilation, the SVD (singular value decomposition) method used in the matrix inversion process of ensemble optimal interpolation is very time-consuming. This paper uses matrix LU decomposition, Choleskey decomposition and QR decomposition respectively to replace singular value decomposition to optimize the matrix inversion process in the ensemble optimal interpolation. Firstly, LU (Choleskey or QR) decomposition breaks down some matrices into two products of triangular matrices (or orthogonal matrices). Secondly, the matrices obtained by decomposition process, are used rapidly to calculate the inverse of matrix. As the algorithm complexity of LU (Choleskey or QR) decomposition is much smaller than that of the singular value decomposition, the performance of the assimilation program is improved greatly. The numerical experiments show that the three kinds of matrix decomposition methods used in this paper can improve the computational efficiency of the ensemble at least two times compared with the traditional implementation based on singular value decomposition. Furthermore, it should be noted that the Choleskey decomposition makes the entire assimilation program achieve the best performance.

Key words: ocean data assimilation, ensemble optimal interpolation (EnOI), matrix inversion, matrix decomposition, Choleskey decomposition