| Stone Method |
Article Index for Stone |
Website Links For Stone |
Information AboutStone Method |
| CATEGORIES ABOUT STONE METHOD | |
| numerical linear algebra | |
|
The LU decomposition is an excellent general purpose linear equation solver. The biggest disadvantage is that it fail to take advantage of coefficient matrix to be a sparce matrix. The LU decomposition of a sparce matrix is usually not sparse, thus, for large system of equations, LU decomposition may require a prohibitive amount of Memory and Arithmetical Operations . In the Preconditioned Iterative Method s, if the preconditioner matrix M is a good approximation of coefficient matrix '''A''' then the convergence is faster. This brings us to idea of using approximate factorization '''LU''' of '''A''' as the iteration matrix M. A version of incomplete lower-upper decomposition method was proposed by H. L. Stone in 1968. This method is designed for equation system arising from discretisation of partial differential equations and was firstly used for a pentadiagonal system of equation obtained while solving an Elliptic Partial Differential Equation in a Two Dimensional space by a Finite Difference method. The LU approximate decomposition was looked in the same pentadiagonal form as the original matrix (three diagonal for L and three diagonals for '''U''') as the best match of the seven possible equations for the five unknowns for the each row of the matrix. ALGORITHM : For the linear system Ax = b : calculate Incomplete LU factorization of matrix '''A''' :: Ax = ('''M'''-'''N''')x = ('''LU'''-'''N''')x = b |
|
|