非侵入性地近似参数化矩阵幂算法的极限——应用于矩阵逆和对数行列式
Nonintrusive approximation of parametrized limits of matrix power algorithms -- application to matrix inverses and log-determinants
AI总结：
本文研究了通过参数化矩阵幂的极限获得的量（如矩阵逆和对数行列式），在参数呈仿射依赖的情况下，利用经验插值法（EIM）推导出矩阵幂的近似，从而得到非侵入性近似。还推导了所获公式的误差上界，并与经典侵入性和非侵入性近似技术进行了数值比较，结果显示算法在测试用例中表现良好。
摘要：
本文研究了可通过参数化矩阵幂的极限获得的量，例如矩阵逆和对数行列式。在参数呈仿射依赖的假设下，我们利用经验插值法（EIM）推导出这些矩阵幂的近似，从而得到上述极限的非侵入性近似。我们推导了所获公式的误差上界。最后提供了与经典侵入性和非侵入性近似技术的数值比较：在考虑的测试用例中，我们的算法在非侵入性方法中表现良好。
英文摘要：
We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.
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