几类非p-范数及其诱导范数

Several Kinds of Non-Hlder VectorNorms and Their Induced Norms

该文构造了几类非ｐ范数，估计了它们的诱导范数的界；并证明了在方阵情形，这些诱导范数均可应用到有关特征值整体条件数的Ｂａｕｅｒ－Ｆｉｋｅ引理中去。

In this paper, three kinds of non-Hlder vector norms are constructed, and their induced norms are designated as ‖·‖ α,‖·‖ β, and ‖·‖ γ respectively. We show that max i,j|a ij |≤‖A‖ α,‖A‖ β,‖A‖ γ≤mi=1nj=1|a ij |. Furthermore, in the square matrix case, we have ‖ diag (d 1,…,d n)‖ α=‖ diag (d 1,…,d n)‖ β=‖ diag (d 1,…,d n)‖ γ= max i{|d i|}. So norms ‖·‖ α,‖·‖ β, and ‖·‖ γ can all be used in the Bauer-Fike lemma with respect to the total condition number for matrix eigenprob lem.