scholarly journals Randomized block Krylov methods for approximating extreme eigenvalues

2021 ◽  
Author(s):  
Joel A. Tropp
Keyword(s):  
Krylov Methods ◽  
Extreme Eigenvalues

An Experimental Study of Methods for Parallel Preconditioned Krylov Methods

1988 ◽  
Author(s):  
Doug Baxter ◽  
Joel Saltz ◽  
Martin Schultz ◽  
Stan Eisenstat ◽  
Kay Crowley
Keyword(s):  
Experimental Study ◽  
Krylov Methods

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

Sign in / Sign up

Export Citation Format

Share Document