Optimal Methods for Ill-Posed Problems
: With Applications to Heat Conduction
Hansen, "Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems
," Numerical Algorithms, vol.
The method has been used in particular for the solution of discrete ill-posed problems
 and in combination with the L-curve method [11, 12, 13] for the determination of the cut-off.
It is well known that regularization parameter plays a very important role in solving ill-posed problems
, and the effectiveness of a regularization method depends strongly on the choice of the regularization parameter.
The present paper is dedicated to estimations of information complexity for severely ill-posed problems
such as Fredholm's integral equations with smooth kernels.
For more details on ill-posed problems
and regularization methods one can refer to [14-20].
We mention the paper  introduced by Hadamard in the field of ill-posed problems
In this paper, we consider linear discrete ill-posed problems
of the form
To obtain stable solutions for these ill-posed problems
, proper regularization techniques are necessary.
Prof Goncharsky told Holography News[R] that computing CLR images is a complicated mathematical task that involves solving what are called 'ill-posed problems
' (ie mathematical problems where one component is badly defined or variable).
Although the SDM works very well for most linear systems, the SDM does lose some of its luster for some ill-posed problems
like inverse problems, image processing, and box-constrained optimization.