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A new method for computing Moore–Penrose inverse matrices

✍ Scribed by F. Toutounian; A. Ataei

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
339 KB
Volume
228
Category
Article
ISSN
0377-0427

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✦ Synopsis

The Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) has many applications in statistics, prediction theory, control system analysis, curve fitting and numerical analysis. In this paper, an algorithm based on the conjugate Gram-Schmidt process and the Moore-Penrose inverse of partitioned matrices is proposed for computing the pseudoinverse of an m × n real matrix A with m ≥ n and rank r ≤ n. Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that of pseudoinverses obtained by the other methods for large sparse matrices.

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An iterative algorithm for estimating the Moore-Penrose generalized inverse is developed. The main motive for the construction of the algorithm is simultaneous usage of Penrose equations ( 2) and ( 4). Convergence properties of the introduced method as well as their first-order and second-order erro