Hanke deals solely with linear inverse problems, and his treatment differs from the many others by giving comparable weight to the general theory of ill-posed problems
and to details of a variety of applications.
Scherzer, "A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
," Numerische Mathematik, vol.
The traditional paradigm for robotic manipulation is in complete disarray in front of this shift of focus: state-of-the-art grasp planners are targeted towards rigid hands and objects, and attempt to find algorithmic solutions to inherently complex, often ill-posed problems
In the case of discrete ill-posed problems
, a well-known basic property of Krylov iterative methods (which might be considered both an advantage or a disadvantage) is the so-called semi-convergence phenomenon, i.
For solving ill-posed problems
regularizing algorithms containing several variable parameters may be fruitful, because a proper selection of parameters involved sometimes improves the convergence properties, reduces the amount of computation, and provides a wider choice of initial guesses.
Shishatskii, ILL-Posed Problems
of Mathematical Physics and Analysis, Amer.
In addition, as is often the case with ill-posed problems
, the coefficient matrix is highly singular.
In this article we do not deal with ill-posed problems
that arise in many aspects of theoretical or applied mathematics, as this subject demands its own research and work.
Rust, Confidence intervals for inequality-constrained least squares problems, with applications to ill-posed problems
, SIAM J.
The corresponding calculations have been performed with the program NLREG (26), a general-purpose program for solving nonlinear ill-posed problems
The author covers the basics of inverse problems, well-posed and ill-posed problems
, Tikhonov regularization, compact operators and the singular value expansion, Tikhonov regularization with seminorms, and a wide variety of other related subjects over the course of the bookAEs five chapters.