bouligandlandweber

This repository contains implementations of the iterative regularization method described in the paper Bouligand-Landweber iteration for a non-smooth ill-posed problem by Christian Clason and Vũ Hữu Nhự.

Python code

The results in the paper were generated using the provided Python implementation (bouligandlandweber.py) (with Python 3.6.5, Numpy 1.15.1, and Scipy 1.1.0) with the following notable differences to allow faster testing:

1. The current code defaults to N=128, while the reported results were obtained with N=512 (see line 24).

2. Plotting is disabled by default but can be enabled by setting figs = True in line 27.

3. Warm starting is used in the semi-smooth Newton method but can be disabled by replacing F(un,yn) by F(un) in line 140.

To run a representative example (N=128, delta = 1e-4, beta=0.005), run python3 bouligandlandweber.py.

Julia code

We also provide an equivalent Julia (version 1.0) implementation in the module BouligandLandweber.jl. To run the same example, start julia in the same directory as the module and enter

include("./BouligandLandweber.jl")
BouligandLandweber.run_example(128,1e-4,0.005);

(Note that the first time this is done, the Julia code will be compiled to native code; subsequent calls to run_example (even with changed parameters) will then be much faster.)

Reference

If you find this code useful, you can cite the paper as

@article{bouligandlandweber,
    author = {Clason, Christian and Nhu, Vu Huu},
    title = {Bouligand-Landweber iteration for a non-smooth ill-posed problem},
    year = {2018},
    eprinttype = {arxiv},
    eprint = {1803.02290},
}