Xuecheng Tai

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A general technique based on space decomposition and subspace correction is used to solve nonlinear convex minimization problems. The differential of the minimization functional is required to satisfy some growth conditions that are weaker than Lipschitz continuity and strong mono-tonicity. Optimal rate of convergence is proved. If the diierential is(More)
This work presents some space decomposition algorithms for a convex minimization problem. The algorithms has linear rate of convergence and the rate of convergence depends only on four constants. The space decomposition could be a multigrid or domain decomposition method. We explain the detailed procedure in implementing our algorithms for a two-level(More)
A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space(More)
The standard approach for image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. State-of-the-art methods to correct these undesirable effects either have weak convergence guarantees(More)
In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature,(More)
Based on some previous work about the connection between image restoration and fluid dynamics, we apply a two-step algorithm for image denoising. In the first step, we use a splitting scheme to study a nonlinear Stokes equation so that tangent vectors are obtained. We propose a continuous boundary condition in this paper. In the second step, we reconstruct(More)