In this paper, we consider the generalized Kronecker product (GKP) linear system associated with a class of consecutive-rank-descending (CRD) matrices arising from bivariate interpolation problems. Relying on the sign sequences of CRD matrices, we show that the associated GKP linear system is accurately solved with an “ideal” componentwise forward error. In particular, a pleasantly small componentwise relative forward error is provided to illustrate that each component of the solution is computed to high relative accuracy. We then present the sign sequences of generalized Vandermonde matrices to show that the associated GKP linear system is accurately solved with the desired componentwise forward errors. Numerical experiments are performed to confirm the high relative accuracy.

在本文中，我们考虑了与二元插值问题引起的一类连续降序（CRD）矩阵相关的广义Kronecker积（GKP）线性系统。依靠CRD矩阵的符号序列，我们表明相关联的GKP线性系统可以通过“理想的”逐分量前向误差来精确求解。特别是，提供了一个令人愉悦的小分量方向相对前向误差，以说明该解决方案的每个分量都以较高的相对精度进行了计算。然后，我们提出广义范德蒙矩阵的符号序列，以表明相关的GKP线性系统能够准确地求解所需的分量正向误差。进行数值实验以确认较高的相对精度。