The software package REGULARIZATION TOOLS [187], Version 3.1, consists of 53 MATLAB routines for analysis and solution of discrete ill-posed problems. By means of this package, the user can experiment with different regularization strategies, compare them, and draw conclusions that would otherwise require a major programming effort. In addition to the analysis and solution routines, the package also includes 12 test problems. The package, as well as the corresponding manual [186], is available from Netlib in the file numeralgo/na4, as well as from the author.

The purpose of REGULARIZATION TOOLS is to provide the user with easy-to-use routines, based on numerically robust and efficient algorithms, for doing experiments with regularization of discrete ill-posed problems. By means of this package, the user can experiment with different regularization strategies, compare them, and draw conclusions that would otherwise require a major programming effort. For discrete ill-posed problems, which are indeed difficult to treat numerically, such an approach is superior to a single black-box routine.

There have been other attempts to write general software for discrete ill-posed problems, all of them implementing Tikhonov regularization. They are listed here in chronological order.

• What appears to be the first package was written in the object-oriented language Simula by Eld n [99], and it concentrated on the use of bidiagonalization ( 5.1.1) and standard-form transformation ( 2.3.1) to solve the Tikhonov problem in its three incarnations (5.1), (5.14), and (5.15).

• The Fortran program CONTIN by Provencher [288] uses the quadrature method to discretize the integral equation (1.2). Equality...