an:06477412
Zbl 1329.65079
Yamashita, Takumi; Kimura, Kinji; Yamamoto, Yusaku
A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix
EN
Numer. Algorithms 69, No. 4, 893-912 (2015).
00347124
2015
j
65F15 15A18 15A42 65F50
singular values; lower bounds; bidiagonal matrix; matrix trace; subtraction-free formula; algorithm; numerical experiment
Traces of inverse powers of a matrix \(BB^T\) determine lower bounds of the smallest singular value of an upper bidiagonal matrix \(B\) with positive entries on both diagonals. Several approaches to the computation of these traces have been studied previously, including one subtraction-free formula. This paper derives another subtraction-free formula different from the previous one. An algorithm for its computation is presented. A comparison of computational costs shows that the evaluation of the new formula requires less operations than the previously proposed one. An efficient implementation of the algorithm for the special case of the second power is included. Numerical experiments conclude the paper.
Iveta Hnetynkova (Praha)