Two Discrete Ill-Posed Problems

Bert W. Rust and Dianne P. O'Leary

This directory specifies two test problems used in
Residual periodograms for choosing regularization parameters for ill-posed problems,
by Bert W. Rust and Dianne P. O'Leary.

Problem 1: The Modified Phillips Problem This problem is specified by the Matlab code phillipsmod.m

Problem 2: The Burrus Problem

This problem arose in measurements of nuclear radiation spectra (W. Burrus and V. Berbinski, Fast neutron spectrosopy with thick organic scintillators, Nuclear Instruments and Methods 67 (1969) pp 181-196).

The data used by Burrus and Verbinski are stored in three files:

  • burrus_K containing the matrix 113 x 77 matrix K.
  • burrus_y containing the matrix 113 x 1 vector y.
  • burrus_S containing the 113 diagonal entries of the 113 x 113 matrix S of standard deviations of the errors in y.
  • t-mesh containing 113 points at which the data was measured.
  • xi-mesh containing 77 points at which the solution should be computed.

    • Each file has one number per line, and the matrix K is given column-by-column.

    To enter the data into Matlab, use the following commands:

    fid = fopen('burrus_K','r');
    a = fscanf(fid,'%f');
    K = reshape(a,113,77);
    clear a

    fid = fopen('burrus_y','r');
    y = fscanf(fid,'%f');

    fid = fopen('burrus_S','r');
    Sdiag = fscanf(fid,'%f');

    fid = fopen('t-mesh','r');
    t = fscanf(fid,'%f');

    fid = fopen('xi-mesh','r');
    xi = fscanf(fid,'%f');