Р. Г. Стронгина. Ниж- ний Новгород: Изд-во Нижегородского университета, 2002, 217 с
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| 5. LDL
T Factorization for Symmetric Indefinite Matrices It is well-known that the Cholesky factorization can fail for symmetric indefinite matrices. In this case some pivoting strategy can be applied (e. g. 184 the Bunch-Kaufman pivoting [6, §4.4]). The algorithm is formulated in [4, 6, 13, 17]. As a, result we get PAP T = LDL T . where L is unit lower triangular, D is block diagonal with 1×1, or 2×2 blocks, and P is a permutation matrix. Now let us look at a recursive formulation of this algorithm. This is given below. The recursion is done on the second dimension of matrix A, i.e. the algorithm works on full columns like in the LU factorization. The LAWRA project on LDL T is still going on. We have developed several perturbation approach algorithms for solving linear systems of equa- tions, where the matrix is symmetric and indefinite. The results are pre- sented in two papers, [7, 12]. We have also obtained very good results for the Bunch-Kaufman fac- torization, where the matrix A is given in packed data format with about 5% extra space appended. We call it a blocked version. The recursion is not applied. The speed of our packed blocked algorithm is comparable with the speed of LAPACK full storage algorithm. The algorithm is described and the comparison performance results for the factorization and solution are presented in [11]. жүктеу/скачать 1,64 Mb. Достарыңызбен бөлісу:
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