On computing accurate singular values and eigenvalues of acyclic matrices
By: J.W. Demmel, W.B. Gragg
Contributors: Gragg, William B.; Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1992
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 12
Subjects: COMPUTATIONS; EIGENVALUES; MATRICES(MATHEMATICS)
Other titles: NPS-MA-92-010.
Description: It is known that small relative perturbations in the entries of a bidiagonal matrix only cause      small relative perturbations in its singular values, independent of the values of the matrix      entries. In this paper we show that a matrix has this property if and only if its associated      bipartite graph is acyclic. We also show how to compute the singular values of such a matrix      to high relative accuracy. The same algorithm can compute eigenvalues of symmetric acyclic      matrices with tiny component-wise relative backward error. This class includes tridragonal      matfices, arrow matrices, and exponentially many others.
Notes: Title from cover.

"NPS-MA-92-010."

"August 1992."

AD A255 892.

Includes bibliographical references (p. 11-12).

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