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- W1990695571 abstract "Lower bounds for the distance of a complex $n times n$ matrix A from the variety of normal matrices are established. The weaker version gives a lower bound of the form ${operatorname{dep}} ( A )/sqrt{n}$, where ${operatorname{dep}}( A )$ is Henrici’s “departure from normality.” Recall that ${operatorname{dep}}( A )$ itself is an upper bound for the distance at issue. The tighter bound contains n diagonal sums coming from the Schur form, hence its computational cost is larger; however, it is attainable. The main result is showing this property. To this end some lemmas concerning normal and triangular matrices are needed, and a set of triangular and (closest) normal matrices with properties of independent interest is introduced." @default.
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- W1990695571 date "1994-07-01" @default.
- W1990695571 modified "2023-09-23" @default.
- W1990695571 title "An Attainable Lower Bound for the Best Normal Approximation" @default.
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- W1990695571 doi "https://doi.org/10.1137/s0895479892232303" @default.
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