Search Results - Numerical solutions of ill-posed problems in abstract spaces

Hanke–Raus rule for Landweber iteration in Banach spaces by Real, Rommel R.

“…We consider the Landweber iteration for solving linear as well as nonlinear inverse problems in Banach spaces…”
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Fractional Tikhonov regularization for linear discrete ill-posed problems by Hochstenbach, Michiel E., Reichel, Lothar

“…Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix…”
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An efficient Legendre-Galerkin spectral method for ill-posed partial differential equations in a bounded domain by Wang, Haowen, Yao, Guoqing

“… Furthermore, we analyze both the error in the approximate analytical solution of the backward parabolic equation and the numerical error associated with the Legendre-Galerkin spectral method…”
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Improved Accuracy Estimation of the Tikhonov Method for Ill-Posed Optimization Problems in Hilbert Space by Kokurin, M. M.

“…The Tikhonov method is studied as applied to ill-posed problems of minimizing a smooth nonconvex functional…”
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Iterative Fejér Processes in Ill-Posed Problems by Vasin, V. V.

“…A brief survey is given concerning iterative processes of Fejér type for basic statements of ill-posed problems, including constrained quadratic and convex…”
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Subspace-restricted singular value decompositions for linear discrete ill-posed problems by Hochstenbach, Michiel E., Reichel, Lothar

“…The truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems…”
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A New Algorithm for a Posteriori Error Estimation for Approximate Solutions of Linear Ill-Posed Problems by Leonov, A. S.

“…A new algorithm for a posteriori estimation of the error in solutions to linear operator equations of the first kind in a Hilbert space is proposed and justified…”
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Solution of Ill-Posed Nonconvex Optimization Problems with Accuracy Proportional to the Error in Input Data by Kokurin, M. Yu

“…The ill-posed problem of minimizing an approximately specified smooth nonconvex functional on a convex closed subset of a Hilbert space is considered…”
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On Constructing a Gradient Quadratic Optimization Method that is Optimal in Terms of Distance to the Exact Solution by Pletnev, N. V.

“…Quadratic optimization problems in Hilbert space often arise when solving ill-posed problems for differential equations…”
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On the second-order asymptotical regularization of linear ill-posed inverse problems by Zhang, Y., Hofmann, B.

“…) method for the stable approximate solution of ill-posed linear operator equations in Hilbert spaces, which are models for linear inverse problems with applications in the natural sciences, imaging and engineering…”
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Convergence analysis of discrete modified Newton scheme for solving ill-posed problems: Convergence analysis of discrete modified Newton by Rajan, M. P., Pradeep, D.

“… In practice, most of these problems are ill-posed, and computing solutions to such problems in an efficient manner is challenging and has been of greatest interest among researchers in the recent past…”
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GKB-FP: an algorithm for large-scale discrete ill-posed problems by Bazán, Fermín S. Viloche, Borges, Leonardo S.

“…We describe an algorithm for large-scale discrete ill-posed problems, called GKB-FP, which combines the Golub-Kahan bidiagonalization algorithm with Tikhonov regularization in the generated Krylov…”
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A fast iterative regularization method for ill-posed problems by Bechouat, Tahar

“…Ill-posed problems manifest in a wide range of scientific and engineering disciplines…”
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Simplified Levenberg-Marquardt method in Banach spaces for nonlinear ill-posed operator equations by Mahale, Pallavi, Shaikh, Farheen M.

“…In 2011, Jin Qinian has proposed a Levenberg-Marquardt method, by making use of duality mapping and the Bregman distance, to get an approximate solution of a nonlinear ill-posed operator equation…”
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Wavelet-based multilevel methods for linear ill-posed problems by Klann, E., Ramlau, R., Reichel, L.

“…The representation of linear operator equations in terms of wavelet bases yields a multilevel framework, which can be exploited for iterative solution…”
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Regularization matrices for discrete ill‐posed problems in several space dimensions by Dykes, Laura, Huang, Guangxin, Noschese, Silvia, Reichel, Lothar

“…‐posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space dimensions…”
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Extended Newton-type iteration for nonlinear ill-posed equations in Banach space by Sreedeep, C. D., George, Santhosh, Argyros, Ioannis K.

“…In this paper, we study nonlinear ill-posed equations involving m -accretive mappings in Banach spaces…”
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Eigenvalue-Based Approaches for Solving an Ill-Posed Problem Arising in Sensor Orientation by Terlemezoglu, Bilgi, Topan, Huseyin

“… Independently of the orientation model, an ill-posed problem is occurred in the adjustment process, caused by the ill-conditioned Jacobian matrix which is differentiated through the orientation elements…”
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A Regularization Parameter in Discrete Ill-Posed Problems by REGINSKA, T

“…The Tikhonov regularization method for discrete ill-posed problems is considered…”
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Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections by Flemming, Jens

“…Numerical solution of ill-posed operator equations requires regularization techniques…”
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