4 papers
A polynomial dimension-dependence analysis of Bramble--Pasciak--Xu preconditioners
Boou Jiang, Jongho Park, Jinchao Xu
We investigate the dimension dependence of Bramble--Pasciak--Xu (BPX) preconditioners for high-dimensional partial differential equations and establish that the condition numbers o…
Auxiliary space theory for the analysis of iterative methods for semidefinite linear systems
Jongho Park, Jinchao Xu
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting…
Variational estimates for Schur complements of symmetric saddle point problems
Jongho Park
We present sharp variational estimates for the extremal eigenvalues of Schur complements arising in symmetric saddle point problems. These estimates make explicit the role of right…
Subspace correction as a general framework for convex optimization algorithms
Boou Jiang, Jongho Park, Jinchao Xu
This paper shows that subspace correction methods provide a common algorithmic and theoretical foundation for several classes of convex optimization algorithms, including operator…