标题： 矩阵函数的块有理Krylov近似误差公式 显示英文标题

标题： Error formulas for block rational Krylov approximations of matrix functions

摘要： 本文研究了与矩阵函数的块有理Krylov近似相关的误差的显式表达式。提出了两种公式，二者均源自块FOM残差的特征描述。第一个公式采用了一种块广义残差多项式，而第二个则利用了残差的块共线性。基于已知的自变量谱信息推导并测试了后验误差界的一组例子。值得注意的是，这两种误差公式及其相应的上界在实际评估时无需使用数值积分。 显示英文摘要

摘要： This paper investigates explicit expressions for the error associated with the block rational Krylov approximation of matrix functions. Two formulas are proposed, both derived from characterizations of the block FOM residual. The first formula employs a block generalization of the residual polynomial, while the second leverages the block collinearity of the residuals. A posteriori error bounds based on the knowledge of spectral information of the argument are derived and tested on a set of examples. Notably, both error formulas and their corresponding upper bounds do not require the use of quadratures for their practical evaluation.