1. PicardREG : A MATLAB package for solving discrete linear ill-posed problems with general-form Tikhonov regularization using the Picard parameter developed by Eitan Levin and Alexander Meltzer. This package picardreg.zip supplements the manuscript titled “Estimation of the regularization parameter in linear discrete ill-posed problems using the Picard parameter”. The script
CompareMethods.m was used to generate the boxplots presented in the manuscript. For more information, see the readme file.
Note: The functions
get_l.m, gravity.m, heat.m, phillips.m from Hansen's Regularization Tools and the function
estimate_Picard_Param.m from O'Leary's spectral filtering package are required to be in MATLAB’s path.
2. MagInverter : A MATLAB package for determination of current density in thin films from the Biot-Savart law developed by Eitan Levin and Alexander Meltzer. This package maginverter2d.zip supplements the manuscript titled “Reconstruction of two-dimensional currents in a thin film from magnetic field measurement”. In addition we provide the package maginverter1d.zip for 1D reconstructions. For a tutorial for these packages see our guide.
3. PicardDF : A MATLAB package for iterative inversion of large scale linear ill-posed problems using the Golub-Kahan bidiagonalization developed by Eitan Levin and Alexander Meltzer. The package fftfiltering.zip features a novel data filter implemented in the function filterDataPicardPPS.m based on applying the Picard parameter to the Fourier transform of the data. This package supplements the manuscript titled “Stopping criterion for iterative regularization of large-scale ill-posed problems using the Picard parameter”.
4. Schwarz Functions : A Matlab code that exemplifies the calculation and utilization of the Schwarz functions described in the paper "An accurate approximation of exponential integrators for the Schrodinger equation" by A. Y. Meltzer. The code reproduces the ETDRK4 curve of figure 3.
Note: The external function "cheb.m" (https://people.maths.ox.ac.