Symbolic computation of the Moore-Penrose inverse using the LDL decomposition of the polynomial matrix
The full-rank LDL* decomposition of a polynomial Hermitian matrix is examined. Explicit formulae are given evaluating the coefficients of matrices 𝑙𝑖𝑗and 𝑑𝑗𝑗. Also, a new method is developed, based on the 𝐿𝐷𝐿* factorization of the matrix product 𝐴*𝐴, for symbolic computation of the Moore-Penrose inv...
Saved in:
| Published in: | Filomat Vol. 27; no. 8; pp. 1393 - 1403 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Faculty of Sciences and Mathematics, University of Niš
01-01-2013
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The full-rank LDL* decomposition of a polynomial Hermitian matrix is examined. Explicit formulae are given evaluating the coefficients of matrices 𝑙𝑖𝑗and 𝑑𝑗𝑗. Also, a new method is developed, based on the 𝐿𝐷𝐿* factorization of the matrix product 𝐴*𝐴, for symbolic computation of the Moore-Penrose inverse matrix. The paper follows the results of [I.P. Stanimirović, M.B. Tasić,Computation of generalized inverses by using the𝐿𝐷𝐿*decomposition, Appl. Math. Lett., 25 (2012), 526–531], where the matrix products 𝐴*𝐴, 𝐴𝐴* and the corresponding 𝐿𝐷𝐿* factorizations are considered in order to compute the generalized inverse of 𝐴. |
|---|---|
| ISSN: | 0354-5180 2406-0933 |
| DOI: | 10.2298/FIL1308393T |