Some properties and generation methods of integer matrices with large condition number (回路とシステム) CAS2010-3 Some properties and generation methods of integer matrices with large condition number
We study about an ill-conditioned integer matrix A = [α_<ij>] with |α_<ij>| ≦ μ. Let n be the order of A. We first give some upper bounds of the condition number of A in terms of Σ_<i,j>α^2_<ij>, μ and n. Next we point out some problems arising in the previous generation methods of extremely ill-conditioned matrices. Finally to solve the above problems we propose a desirable singular value distribution of ill-conditioned benchmark matrices and give partial solutions to them.