dc.contributor.author | Stewart, G. W. | en_US |
dc.date.accessioned | 2004-05-31T22:49:34Z | |
dc.date.available | 2004-05-31T22:49:34Z | |
dc.date.created | 1998-01 | en_US |
dc.date.issued | 1998-10-15 | en_US |
dc.identifier.uri | http://hdl.handle.net/1903/934 | |
dc.description.abstract | The adjoint $A\adj$ of a matrix $A$ is the transpose of the matrix of the
cofactors of the elements of $A$. The computation of the adjoint from
its definition involves the computation of $n^{2}$ determinants of
order $(n-1)$\,---\,a prohibitively expensive $O(n^{4})$ process.
On the other had the computation from the formula $A\adj =
\det(A)A\inv$ breaks down when $A$ is singular and is potentially
unstable when $A$ is ill-conditioned. In this paper we first show
that the ajdoint can be perfectly conditioned, even when $A$ is
ill-conditioned. We then show that if due care is taken the adjoint
can be accurately computed from the inverse, even when the latter has
been inaccurately computed. In an appendix to this paper we establish
a folk result on the accuracy of computed inverses.
\end{minipage}
\end{center}
Also cross-referenced as UMIACS-TR-98-02 | en_US |
dc.format.extent | 164081 bytes | |
dc.format.mimetype | application/postscript | |
dc.language.iso | en_US | |
dc.relation.ispartofseries | UM Computer Science Department; CS-TR-3864 | en_US |
dc.relation.ispartofseries | UMIACS; UMIACS-TR-98-02 | en_US |
dc.title | On the Adjoint Matrix | en_US |
dc.type | Technical Report | en_US |
dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_US |
dc.relation.isAvailableAt | University of Maryland (College Park, Md.) | en_US |
dc.relation.isAvailableAt | Tech Reports in Computer Science and Engineering | en_US |
dc.relation.isAvailableAt | UMIACS Technical Reports | en_US |