Spectral sensitivity of products of bidiagonals Original Research Article

Simple formulae are derived for certain relative condition numbers. Tridiagonal matrices may be represented as products of bidiagonals in various ways depending on properties such as symmetry and positive definiteness. The condition numbers give the amplification factor for relative changes in a nonzero eigenvalue caused by relative changes in an entry of a bidiagonal factor. The formulae show that in many, but not all cases these condition numbers are of modest size. Several examples illustrate the results and raise new questions.