论文标题
操作员平方根的高斯方法
A Gaussian method for the operator square root
论文作者
论文摘要
我们考虑了希尔伯特空间中定期积聚运算符的反平方根的近似值。近似是有理类型的，它来自应用于该问题的特殊积分公式的高斯 - legendre规则。根据数值范围的使用，我们得出了急剧误差估计，并提供了一些数值实验。出于实际目的，还考虑了有限维度的情况。在这种情况下，收敛性显示为指数类型。
We consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. The approximation is of rational type and comes from the use of the Gauss-Legendre rule applied to a special integral formulation of the problem. We derive sharp error estimates, based on the use of the numerical range, and provide some numerical experiments. For practical purposes, the finite dimensional case is also considered. In this setting, the convergence is shown to be of exponential type.
