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- W2886939563 abstract "Abstract Recently Brent et al. presented new estimates for the determinant of a real perturbation I + E of the identity matrix. They give a lower and an upper bound depending on the maximum absolute value of the diagonal and the off-diagonal elements of E, and show that either bound is sharp. Their bounds will always include 1, and the difference of the bounds is at least tr ( E ) . In this note we present a lower and an upper bound depending on the trace and Frobenius norm ϵ : = ‖ E ‖ F of the (real or complex) perturbation E, where the difference of the bounds is not larger than ϵ 2 + O ( ϵ 3 ) provided that ϵ 1 . Moreover, we prove a bound on the relative error between det ( I + E ) and exp ( tr ( E ) ) of order ϵ 2 ." @default.
- W2886939563 created "2018-08-22" @default.
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- W2886939563 date "2018-12-01" @default.
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- W2886939563 title "Estimates of the determinant of a perturbed identity matrix" @default.
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- W2886939563 doi "https://doi.org/10.1016/j.laa.2018.08.009" @default.
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