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Full-rank block LDL decomposition and the inverses of n× n block matrices.
- Source :
- Journal of Applied Mathematics & Computing; Oct2012, Vol. 40 Issue 1/2, p569-586, 18p
- Publication Year :
- 2012
-
Abstract
- Full-rank block LDL decomposition of a Hermitian n× n block matrix A is examined, where the iterative procedure evaluating the sub-matrices appearing in L and D is provided. This factorization is used to evaluate the inverse and Moore-Penrose inverse of a Hermitian n× n block matrix. The method for the calculation of the Moore-Penrose inverse of an arbitrary 2×2 block matrix is also provided. Therefore, matrix products A A and AA and the corresponding full-rank block LDL factorizations are observed. Also, a simple explicit formulae calculating the solution vector components of the normal system of equations is stated, where the LDL decomposition of the system matrix is done. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15985865
- Volume :
- 40
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Journal of Applied Mathematics & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 79629135
- Full Text :
- https://doi.org/10.1007/s12190-012-0579-3