Computing low-rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods

08/29/2020
by   Peter Kandolf, et al.
0

The Fréchet derivative L_f(A,E) of the matrix function f(A) plays an important role in many different applications, including condition number estimation and network analysis. We present several different Krylov subspace methods for computing low-rank approximations of L_f(A,E) when the direction term E is of rank one (which can easily be extended to general low-rank). We analyze the convergence of the resulting method for the important special case that A is Hermitian and f is either the exponential, the logarithm or a Stieltjes function. In a number of numerical tests, both including matrices from benchmark collections and from real-world applications, we demonstrate and compare the accuracy and efficiency of the proposed methods.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset