Matrices with characteristic features of discrete ill-posed problems, collected by P. C. Hansen.
The following description comes from the Regularization Tools Manual
which is at http://www2.imm.dtu.dk/~pch/Regutools/RTv4manual.pdf.
These matrices are from the built-in test problems in Regularization Tools
(see http://www2.imm.dtu.dk/~pch/Regutools/). All of the matrices included
below are taken from the literature (see the Regularization Tools Manual
for references). All of them have in common that they are easy to generate,
and they share the characteristic features, discussed in Chapter 2 of the
Regularization Tools Manual, of discrete ill-posed problems.
All the test problems are derived from discretizations of a Fredholm integral
equation of the first kind. Two different discretization techniques are used:
the quadrature method and the Galerkin method with orthonormal basis functions.
For both methods the product Ax is, in general, different from b.
The test problems that are included in the SJsingular data base are:
baart: Fredholm integral equation of the first kind.
foxgood: severely ill-posed problem.
gravity: 1-D gravity surveying model problem
heat: inverse heat equation.
i_laplace: inverse Laplace transformation.
parallax: Stellar parallax problem with 28 fixed, real observations.
shaw: one-dimensional image restoration model.
tomo: a 2D tomography test problem.
ursell: integral equation with no square integrable solution.
wing: problem with a discontinuous solution.