The Bunch–Kaufman factorization of symmetric matrices signature similar to sign regular matrices

The Bunch–Kaufman pivoting strategy is a most commonly used method in practice to factor symmetric indefinite matrices. However, this method in general may destroy the band structure of banded matrices, and its growth factor bound of (2.57)n-1 can almost be attained. In this paper, we investigate the behavior of the method for factorizing symmetric indefinite matrices that are signature similar to sign regular matrices with signature ∊. The growth factor bound depending on flips in the signature ∊ is derived. For factorizing such banded matrices, if the Bunch-Kaufman pivoting strategy is modified as suggested by Sorensen and Van Loan, then not only do the same growth factor bounds hold, but also the bandwidth is nicely preserved.