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…
Unified analysis of saddle point problems via auxiliary space theory
Jongho Park
We present sharp estimates for the extremal eigenvalues of the Schur complements arising in saddle point problems. These estimates are derived using the auxiliary space theory, in…
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…
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…