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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 016 719 360
Author(s):
Rojo, O.; Soto, R.; Egana, J.:
Shorttitle:
Construction of a positive oscillatory matrix with a prescribed spectrum
Source:
Comput. Math. Appl. 41, Noo. 3 - 4, 353 - 361 (2001).
Classification:
Primary Classification:
65F18Inverse eigenvalue problems
Secondary Classification:
15A29Inverse problems
Keywords:
totally positive matrices; oscillatory matrices; inverse eigenvalue problem; matrices of minors;
Review:

Small vibrations of elastic systems are closely related to the so
called oscillatory matrices A of order n, and the paper offers a
new re-construction of an A from its decreasing n-plet of positive
eigenvalues. There are several key ideas used: firstly the fact
that the (n-1)-st power of the tridiagonal A is totally positive,
secondly a trick re-parametrizing the spectrum and giving the
related auxiliary T whose (n-1)-compound matrix is shown to be the
desired new, cheaper and numerically stable representation of A.

Remarks to the editors:

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