# Compress‐and‐restart block Krylov subspace methods for Sylvester matrix equations

@article{Kressner2020CompressandrestartBK, title={Compress‐and‐restart block Krylov subspace methods for Sylvester matrix equations}, author={Daniel Kressner and Kathryn Lund and Stefano Massei and Davide Palitta}, journal={Numerical Linear Algebra with Applications}, year={2020}, volume={28} }

Block Krylov subspace methods (KSMs) comprise building blocks in many state‐of‐the‐art solvers for large‐scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov subspace methods provide a major reduction in iteration counts over polynomial block KSMs, they also require reliable solvers for the coefficient matrices, and these solvers are often iterative methods themselves. It is not hard to devise…

## 2 Citations

### On an integrated Krylov-ADI solver for large-scale Lyapunov equations

- Computer ScienceNumerical Algorithms
- 2022

This work illustrates how a single approximation space can be constructed to solve all the shifted linear systems needed to achieve a prescribed accuracy in terms of Lyapunov residual norm and shows how to fully merge the two iterative procedures to obtain a novel, efficient implementation of the low-rank ADI method.

### Limited‐memory polynomial methods for large‐scale matrix functions

- Computer Science, MathematicsArXiv
- 2020

Various limited‐memory methods for the approximation of the action of a large‐scale matrix function on a vector are reviewed, with emphasis on polynomial methods, whose memory requirements are known or prescribed a priori.

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