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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 018 027 917
Author(s):
Xie, Dongxiu; Hu, Xiyan; Zhang, Lei:
Shorttitle:
The solvability conditions for inverse eigenvalue problem of anti-bisymmetric matrices.
Source:
J. Comput. Math. 20, No. 3, 245 - 256 (2002).
Classification:
65F05Direct methods for linear systems and matrix inversion
Primary Classification:
15A29Inverse problems
Secondary Classification:
65F18Inverse eigenvalue problems
Keywords:
Inverse eigenvalue problem; Frobenius norm; approximate solution by a real bi-antisymmetric matrix
Review:

Among all the inverse eigenvalue problems the authors pick up the
following two. Problem I: Given X (= m complex eigenvectors of some
A) and knowing the m related complex eigenvalues, search for A in the
class of the so called anti-bisymmetric n by n real matrices (i.e.,
matrices which are anti-symmetric with respect to both main
diagonals). Problem II: Over the solution set, find an element with
the minimal distance (in the sense of Frobenius norm) from a given
real matrix. In the second context, the authors construct the
solution set and give the expression for the solution, separating the
even and odd dimensions n. In the former problem, they also add some
necessary and sufficient conditions of its solvability.
Remarks to the editors:

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