منابع مشابه
Sobolev Gradients: Introduction, Applications, Problems
Sobolev gradient is defined and a simple example is given. A number of applications are described. A number of problems are stated, some of which are open problems for research.
متن کاملSobolev Gradients and the Ginzburg-Landau Functional
We describe a Sobolev gradient method for finding minima of the Ginzburg–Landau functional for superconductivity. This method leads to a particularly simple algorithm which avoids consideration of the nonlinear boundary conditions associated with the Ginzburg–Landau equations.
متن کاملNonlinear least squares and Sobolev gradients
Least squares methods are effective for solving systems of partial differential equations. In the case of nonlinear systems the equations are usually linearized by a Newton iteration or successive substitution method, and then treated as a linear least squares problem. We show that it is often advantageous to form a sum of squared residuals first, and then compute a zero of the gradient with a ...
متن کاملGeometric Curve Modeling with Sobolev Gradients
The Sobolev gradient method is a powerful tool for geometric modeling. We treat the problem of constructing fair curves by minimizing a fairness measure subject to geometric constraints. The measure might include curve length, curvature, torsion, and/or variation of curvature. The constraints may include specified values, tangent vectors, and/or curvature vectors. We may also require periodicit...
متن کاملA Levenberg-Marquardt Method based on Sobolev gradients
We extend the theory of Sobolev gradients to include variable metric methods, such as Newton’s method and the Levenberg-Marquardt method, as gradient descent iterations associated with stepwise variable inner products. In particular, we obtain existence, uniqueness, and asymptotic convergence results for a gradient flow based on a variable inner product.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04251-8