6 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…
Sharp inf-sup estimate for the Stokes equation in tight domains with periodic pillars and some numerical implications
Qi Xin, Shihua Gong, Jinchao Xu
The predictive simulation of fluid dynamics in densely packed microfluidic devices, such as Deterministic Lateral Displacement (DLD) arrays, stagnates with standard iterative solve…
Randomized subspace correction methods for convex optimization
Boou Jiang, Jongho Park, Jinchao Xu
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms,…
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…
Randomized Greedy Algorithms for Neural Network Optimization
Jinchao Xu, Xiaofeng Xu
Greedy algorithms have been successfully analyzed and applied in training neural networks for solving variational problems, ensuring guaranteed convergence orders. In this paper, w…