A new subtraction-free formula for lower bounds of the minimal singular   value of an upper bidiagonal matrix
  Traces of inverse powers of a positive definite symmetric tridiagonal matrix give lower bounds of the minimal singular value of an upper bidiagonal matrix. In a preceding work, a formula for the traces which gives the diagonal entries of the inverse powers is presented. In this paper, we present another formula which gives the traces based on a quite different idea from the one in the preceding work. An efficient implementation of the formula for practice is also presented. 
Takumi Yamashita, Kinji Kimura and Yusaku Yamamoto
math.NA