  Jacobi matrices are parametrized by their eigenvalues and norming constants
(first coordinates of normalized eigenvectors): this coordinate system breaks
down at reducible tridiagonal matrices. The set of real symmetric tridiagonal
matrices with prescribed simple spectrum is a compact manifold, admitting an
open covering by open dense sets ${\cal U}^\pi_\Lambda$ centered at diagonal
matrices $\Lambda^\pi$, where $\pi$ spans the permutations. {\it Bidiagonal
coordinates} are a variant of norming constants which parametrize each open set
${\cal U}^\pi_\Lambda$ by the Euclidean space.
  The reconstruction of a Jacobi matrix from inverse data is usually performed
by an algorithm introduced by de Boor and Golub. In this paper we present a
reconstruction procedure from bidiagonal coordinates and show how to employ it
as an alternative to the de Boor-Golub algorithm. The inverse bidiagonal
algorithm rates well in terms of speed and accuracy.
