5 papers · 1 filter
Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices with block-triangular preconditioners
Luca Bergamaschi, Michele Bergamaschi, John W. Pearson
We develop eigenvalue bounds for symmetric, block-tridiagonal multiple saddle-point linear systems, preconditioned with block-triangular matrices, based on approximate Schur comple…
Carleman Linearization of Parabolic PDEs: Well-posedness, convergence, and efficient numerical methods
Bernhard Heinzelreiter, John W. Pearson
We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate…
Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices
L. Bergamaschi, A. Martinez, J. W. Pearson +1
We develop eigenvalue bounds for symmetric, block tridiagonal multiple saddle-point linear systems, preconditioned with block diagonal matrices. We extend known results for $3 \tim…
A Framework for the Solution of Tree-Coupled Saddle-Point Systems
Christoph Hansknecht, Bernhard Heinzelreiter, John W. Pearson +1
We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then…
Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization
Luca Bergamaschi, Angeles Martinez, John Pearson +1
In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear sy…