This paper is concerned with the approximation of matrix functionals of the form w^Tf(A)v, where \(A\in \mathbb {R}^{n\times n}\) is a large nonsymmetric matrix, \(\boldsymbol {w},\boldsymbol {v}\in \mathbb {R}^{n}\), and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.

中文翻译：

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非对称矩阵泛函的Gauss-Laurent型正交规则

本文关注w ^T f（A）v形式的矩阵泛函的近似，其中\（A \ in \ mathbb {R} ^ {n \ times n} \）是一个大的非对称矩阵\（\ \ mathbb {R} ^ {n} \中的oldsymbol {w}，\ boldsymbol {v} \），并且f是使f（A）定义明确的函数。我们导出了这些函数的近似值的高斯-洛朗特正交规则，并且还开发了相关的反高斯-洛朗特正交规则，这些规则使我们能够估计高斯-洛朗特规则的正交误差。计算示例说明了所描述的正交规则的性能。