This article shows that the bidiagonal decomposition of many important matrices of q-integers can be constructed to high relative accuracy (HRA). This fact can be used to compute with HRA the eigenvalues, singular values, and inverses of these matrices. These results can be applied to collocation matrices of q-Laguerre polynomials, q-Pascal matrices, and matrices formed by q-Stirling numbers. Numerical examples illustrate the theoretical results.

中文翻译：

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q 整数矩阵的高相对精度

这篇文章表明，许多重要的q整数矩阵的双对角分解可以构造为高相对精度 (HRA)。这一事实可用于使用 HRA 计算这些矩阵的特征值、奇异值和逆。这些结果可以应用于q -Laguerre 多项式、q -Pascal 矩阵和由q -Stirling 数形成的矩阵的搭配矩阵。数值例子说明了理论结果。