Construction of Real Band Anti-Symmetric Matrices from Spectral Data

In this paper,we describe how to construct a real anti-symmetric(2p-1)-band matrix with prescribed eigenvalues in its ρ leading principal submatrices.This is done in two steps.First,an anti-symmetric matrix B is constructed with the specified spectral data but not necessary a band matrix.Then B is transformed by Householder transformations to a (2ρ-1)-band matrix with the prescribed eigenvalues.An algorithm is presented.Numerical results are presented to demonstrate that the proposed method is effective.

In this paper, we describe how to construct a real anti-symmetric （2p- 1）-band matrix with prescribed eigenvalues in its p leading principal submatrices. This is done in two steps. First, an anti-symmetric matrix B is constructed with the specified spectral data but not necessary a band matrix. Then B is transformed by Householder transformations to a （2p- 1）-band matrix with the prescribed eigenvalues. An algorithm is presented. Numerical results are presented to demonstrate that the proposed method is effective.