In this paper, a class of quasi-Said-Ball-Vandermonde (q-SBV) matrices belonging to generalized sign regular matrices with signature \((1,\dots ,1,-1)\) is introduced. We first accurately compute all the parameters of q-SBV matrices from their bidiagonal decompositions. Furthermore, an algorithm is proposed for computing all the eigenvalues of q-SBV matrices to high relative accuracy by using the accurate parameters. At last, some numerical experiments are presented to show the efficiency and accuracy of our algorithms.

中文翻译：

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广义符号正则拟Said-Ball-Vandermonde矩阵特征值的精确计算

本文介绍了一类拟 Said-Ball-Vandermonde (q-SBV) 矩阵，属于具有签名\((1,\dots ,1,-1)\) 的广义符号正则矩阵。我们首先通过双对角分解准确计算 q-SBV 矩阵的所有参数。此外，还提出了一种算法，通过使用精确的参数以较高的相对精度计算 q-SBV 矩阵的所有特征值。最后，进行了一些数值实验来展示我们算法的效率和准确性。