一般Toeplitz系统的一个弱稳定算法
A weakly stable algorithm for general Toeplitz systems
摘要：
我们证明了Toeplitz或Hankel矩阵A的QR分解的快速算法在R^T.R接近A^T. A的意义下是弱稳定的。因此，当用该算法求解半正规方程R^T.Rx = A^Tb时，得到了求解非奇异Toeplitz或Hankel线性系Ax = b的弱稳定方法.该算法也适用于解决满秩Toeplitz或Hankel最小二乘问题。
英文摘要：
We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.
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