Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Frank Schöpfer"'
Publikováno v:
Abstract and Applied Analysis, Vol 2008 (2008)
Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest des
Externí odkaz:
https://doaj.org/article/2609ed6c15844aba919413de4ff04c58
Autor:
Frank Schöpfer, Alexey Chernov
Publikováno v:
Journal of Optimization Theory and Applications. 186:169-190
We propose and analyze a global search algorithm for the computation of the minimum zone sphericity (circularity) error of a given set. The formulation is valid in any dimension and covers both finite sets of data points as well as infinite sets like
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6484626ba8ff7bfe5a935f1fa161ca3d
https://doi.org/10.1007/s10957-020-01689-8
https://doi.org/10.1007/s10957-020-01689-8
The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each iteration in comp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f1811a1468c91fa94e27758db1f4ece
A standard solution technique for linear operator equations of first kind is the Landweber scheme which is an iterative method that uses the negative gradient of the current residual as search direction, which is also called the Landweber direction.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87351067e4517c660ad974c6f405abe4
Autor:
Alexey Chernov, Frank Schöpfer
Publikováno v:
Journal of Optimization Theory and Applications. 190:709-710
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cd5be2c9fdf7646f11562561912b026b
https://doi.org/10.1007/s10957-021-01907-x
https://doi.org/10.1007/s10957-021-01907-x
Autor:
Dirk A. Lorenz, Frank Schöpfer
Publikováno v:
Mathematical Programming. 173:509-536
The randomized version of the Kaczmarz method for the solution of consistent linear systems is known to converge linearly in expectation. And even in the possibly inconsistent case, when only noisy data is given, the iterates are expected to reach an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7f09f39e635ed384247ba2365bd097a
https://doi.org/10.1007/s10107-017-1229-1
https://doi.org/10.1007/s10107-017-1229-1
Autor:
Frank Schöpfer
Publikováno v:
SIAM Journal on Optimization. 26:1883-1911
Linear convergence rates of descent methods for unconstrained minimization are usually proved under the assumption that the objective function is strongly convex. Recently it was shown that the weaker assumption of restricted strong convexity suffice
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7756f256cb4bfd37fe82e1a82727c5f8
https://doi.org/10.1137/140992990
https://doi.org/10.1137/140992990
This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact---a situation we refer to as "mismatched adjoint". We show that the method may still converg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f27a612fee5e2ee131e248ee286deb3b
Publikováno v:
SIAM Journal on Imaging Sciences. 7:1237-1262
The linearized Bregman method is a method to calculate sparse solutions to systems of linear equations. We formulate this problem as a split feasibility problem, propose an algorithmic framework based on Bregman projections, and prove a general conve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d65254f668d54165f534c0e1459703e
https://doi.org/10.1137/130936269
https://doi.org/10.1137/130936269
Autor:
Frank Schöpfer
Publikováno v:
SIAM Journal on Optimization. 22:1206-1223
We are concerned with linearly constrained convex programs with polyhedral norm as objective function. Friedlander and Tseng [SIAM J. Optim., 18 (2007), pp. 1326--1350] have shown that there exists an exact regularization parameter for the associated
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3458ea44fff7f3e9e57ece9fba99b729
https://doi.org/10.1137/11085236x
https://doi.org/10.1137/11085236x