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math.NA2025
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…
math.NA2025
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…
math.NA2025
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…