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On a fast and nearly division-free algorithm for the characteristic polynomial (2011.12573v1)
Published 25 Nov 2020 in math.NA and cs.NA
Abstract: We review the Preparata-Sarwate algorithm, a simple $O(n{3.5})$ method for computing the characteristic polynomial, determinant and adjugate of an $n \times n$ matrix using only ring operations together with exact divisions by small integers. The algorithm is a baby-step giant-step version of the more well-known Faddeev-Leverrier algorithm. We make a few comments about the algorithm and evaluate its performance empirically.