中文摘要：

可能，为最不解决的大多数流行规则化方法摆平问题 minxAx - b2 与一高度性恶或评价缺乏的系数矩阵 A 是 Tikhonov 规则化方法。在这份报纸我们在场 normwise 的明确的表情，混合并且当 A 有线性结构时， componentwise 状况为 Tikhonov 规则化数。在非线性的结构的特殊情况中的结构化的条件数字即 Vandermonde 和 Cauchy 矩阵也被考虑。在结构化的条件数字和未组织的条件数字之间的一些比较被数字实验做。另外，我们也导出 normwise，混合并且当系数矩阵，规则化矩阵和右边向量都被使不安时， componentwise 状况为 Tikhonov 规则化数，它概括 Chu 等获得的结果。

英文摘要：

The possibly most popular regularization method for solving the least squares problem rain ‖Ax - b‖2 with a highly ill-conditioned or rank deficient coefficient matrix A is the x Tikhonov regularization method. In this paper we present the explicit expressions of the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when A has linear structures. The structured condition numbers in the special cases of nonlinear structure i.e. Vandermonde and Cauchy matrices are also considered. Some comparisons between structured condition numbers and unstructured condition numbers are made by numerical experiments. In addition, we also derive the normwise, mixed and componentwise condition numbers for the Tikhonov regularization when the coefficient matrix, regularization matrix and right-hand side vector are all perturbed, which generalize the results obtained by Chu et al. [Numer. Linear Algebra Appl., 18 （2011）, 87-103].