The total positivity of collocation, Wronskian and Gram matrices corresponding to bases of the form (e^λt,te^λt,…,tⁿe^λt) is analyzed. A bidiagonal decomposition providing the accurate numerical resolution of algebraic linear problems with these matrices is derived. The numerical experimentation confirms the accuracy of the proposed methods.

中文翻译：

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使用与基数 {tieλt} 相关的矩阵进行准确计算

分析了对应于 ( e ^{λ t} , t e ^{λ t} ,…, t ⁿ e ^{λ t} )形式的基的搭配、Wronskian 和 Gram 矩阵的总正性。推导出使用这些矩阵为代数线性问题提供精确数值分辨率的双对角分解。数值实验证实了所提出方法的准确性。