A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix

作者：Yamashita Takumi^*; Kimura Kinji; Yamamoto Yusaku

来源：Numerical Algorithms, 2015, 69(4): 893-912.

DOI：10.1007/s11075-014-9931-z

• Singular value
• Lower bound
• Trace

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.

• 出版日期2015-8