科研之友
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摘要
It was shown in [T. Ando, Acta Sci. Mat. (Szeged), 34, pp. 11-15] that any matrix A with numerical radius at most 1 is similar to a contraction (a matrix T with spectral norm at most 1) via a similarity transformation with condition number at most 2; that is, A = STS-1, where parallel to T parallel to <= 1 and kappa(S) equivalent to parallel to S parallel to.parallel to S-1 parallel to <= 2. However, no explicit algorithm was given for producing such a similarity transformation; in this paper, we give a method for constructing such similarity transformations. As a side benefit, the algorithm indicates whether the numerical radius of A is greater than 1 (or greater than some given number r(0)) and so can be used to determine (sometimes very quickly) whether the numerical radius is greater than a given value.
- 出版日期2015
