On the Computation of the Moore—Penrose Inverse of Matrices with Symbolic Elements

Karsten Schmidt ()
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Karsten Schmidt: Fakultält Wirtschaftswissenschaften

A chapter in Statistical Inference, Econometric Analysis and Matrix Algebra, 2009, pp 349-358 from Springer

Abstract: Abstract In this paper potential difficulties in using Greville's method for the computation of the Moore—Penrose inverse of a matrix that also contains symbolic elements are discussed. For the actual computation of the Moore—Penrose inverse of matrices whose elements are not numeric only, a Computer Algebra System has to be used. Initially, the computation of the Moore—Penrose inverse of a vector is considered which is a simple task if it only has numeric elements. If it contains symbolic elements, it might also be straightforward, but might turn out to be difficult. As Greville's method — an iterative algorithm that needs n steps for the computation of the Moore—Penrose inverse of an m by n matrix — requires the computation of the Moore—Penrose inverse of a vector in each step, the difficulty just mentioned might prevent the actual computation of the Moore—Penrose inverse of a matrix with symbolic elements.

Keywords: Iterative Algorithm; Actual Computation; Generalize Inverse; Computer Algebra System; Zero Vector (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2121-5_24

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DOI: 10.1007/978-3-7908-2121-5_24

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