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.
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
He has published numerous journal articles in the areas of numerical analysis, operator theory, ordinary and partial differential equations, optimization, and inverse and ill-posed problems
They arise in image deblurring problems as well as from the discretization of linear ill-posed problems
such as Fredholm integral equations of the first kind with a continuous kernel.
Information processing in classical ~von Neumann~ architectures is less efficient compared to biological counterparts when dealing with ill-posed problems
and noisy data.
Mathematicians, geophysicists, and other young scientists from China and abroad, gathered in Beijing during July 2010 for a workshop to discuss how to solve inverse and ill-posed problems
using different solution strategies.
Basing their work on that of the Russian mathematical pioneer Andrei Nikolaevich Tikhonov, the authors explain Russian techniques in inverse mathematical problems, boundary value problems for ordinary differential equations, boundary value problems for elliptic equations, boundary value problems for parabolic equations, solution methods for ill-posed problems
(to which inverse mathematical physics problems often belong), right-hand side identification, evolutionary inverse problems and other problems, including non-local distribution of boundary conditions.