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Computational aspects of the geometric mean of two matrices: a survey
Algorithms for the computation of the (weighted) geometric mean G of two positive definite
matrices are described and discussed. For large and sparse matrices the problem of …
matrices are described and discussed. For large and sparse matrices the problem of …
[HTML][HTML] A rational preconditioner for multi-dimensional Riesz fractional diffusion equations
We propose a rational preconditioner for an efficient numerical solution of linear systems
arising from the discretization of multi-dimensional Riesz fractional diffusion equations. In …
arising from the discretization of multi-dimensional Riesz fractional diffusion equations. In …
Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods
We consider the problem of approximating the von Neumann entropy of a large, sparse,
symmetric positive semidefinite matrix A, defined as tr (f (A)) where f (x)=-x log x. After …
symmetric positive semidefinite matrix A, defined as tr (f (A)) where f (x)=-x log x. After …
Challenges in computing matrix functions
This manuscript summarizes the outcome of the focus groups at" The f (A) bulous workshop
on matrix functions and exponential integrators", held at the Max Planck Institute for …
on matrix functions and exponential integrators", held at the Max Planck Institute for …
Rational Krylov methods for fractional diffusion problems on graphs
In 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 …
equation on directed networks, which can be expressed in terms of the graph Laplacian L as …
A unified rational Krylov method for elliptic and parabolic fractional diffusion problems
We present a unified framework to efficiently approximate solutions to fractional diffusion
problems of stationary and parabolic type. After discretization, we can take the point of view …
problems of stationary and parabolic type. After discretization, we can take the point of view …
Improved ParaDiag via low-rank updates and interpolation
This work is concerned with linear matrix equations that arise from the space-time
discretization of time-dependent linear partial differential equations (PDEs). Such matrix …
discretization of time-dependent linear partial differential equations (PDEs). Such matrix …
Adaptive rational Krylov methods for exponential Runge–Kutta integrators
We consider the solution of large stiff systems of ODEs with explicit exponential Runge–
Kutta integrators. These problems arise from semidiscretized semilinear parabolic PDEs on …
Kutta integrators. These problems arise from semidiscretized semilinear parabolic PDEs on …
Krylov subspace restarting for matrix Laplace transforms
A common way to approximate—the action of a matrix function on a vector—is to use the
Arnoldi approximation. Since a new vector needs to be generated and stored in every …
Arnoldi approximation. Since a new vector needs to be generated and stored in every …
[PDF][PDF] Improved parallel-in-time integration via low-rank updates and interpolation
This work is concerned with linear matrix equations that arise from the space-time
discretization of time-dependent linear partial differential equations (PDEs). Such matrix …
discretization of time-dependent linear partial differential equations (PDEs). Such matrix …