This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the flexibility of adding constraints. In particular, the latter allows us to control specific properties preferred in matrix function evaluation. For example, in the case of a normal matrix, we can guarantee a bound over the condition number of the matrix, which one needs to invert for evaluating the rational matrix function. We demonstrate the efficiency of our approach for several applications of matrix functions based on direct spectrum filtering.
翻译:本文件提出一种独特的优化方法,用于估计最小最大合理近似值及其用于评价矩阵功能。我们的方法使扩展为普遍合理近近值,并具有增加限制的灵活性,特别是后者使我们能够控制矩阵函数评价中偏好的具体属性。例如,在正常矩阵的情况下,我们可以保证矩阵的条件号受约束,在评价合理矩阵功能时需要颠倒。我们展示了我们在基于直接频谱过滤的矩阵功能的若干应用中采用的方法的效率。