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Journal of Applied Mathematics and Computing

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01-10-2012 | Computational mathematics

Full-rank block LDL ^∗ decomposition and the inverses of n×n block matrices

Author: Ivan Stanimirović

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2012

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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.

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Title: Full-rank block LDL ∗ decomposition and the inverses of n×n block matrices
Author: Ivan Stanimirović
Publication date: 01-10-2012
Publisher: Springer-Verlag
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2012
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-012-0579-3

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