Piecewise-uniform regularization of ill-posed problems with discontinuous solutions

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(82)90121-5 ◽

1982 ◽

Vol 22 (3) ◽

pp. 20-36 ◽

Author(s):

A.S. Leonov

Keyword(s):

Discontinuous Solutions ◽

Ill Posed ◽

Uniform Regularization

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Piece-uniform regularization of ill-posed problems with discontinuous solutions

Nonlinear Ill-Posed Problems ◽

10.1007/978-94-017-5167-4_5 ◽

1998 ◽

pp. 255-276

Author(s):

A. N. Tikhonov ◽

A. S. Leonov ◽

A. G. Yagola

Keyword(s):

Discontinuous Solutions ◽

Ill Posed ◽

Uniform Regularization

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Locally extra-optimal regularizing algorithms and a posteriori estimates of the accuracy for ill-posed problems with discontinuous solutions

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542516010127 ◽

2016 ◽

Vol 56 (1) ◽

pp. 1-13 ◽

Author(s):

A. S. Leonov

Keyword(s):

A Posteriori ◽

Discontinuous Solutions ◽

Regularizing Algorithms ◽

Ill Posed ◽

A Posteriori Estimates

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ESTIMATION OF DISCONTINUOUS SOLUTIONS OF ILL-POSED PROBLEMS BY REGULARIZATION FOR SURFACE REPRESENTATIONS: NUMERICAL REALIZATION VIA MOVING GRIDS

Recent Development in Theories and Numerics ◽

10.1142/9789812704924_0007 ◽

2003 ◽

Author(s):

ANDREAS NEUBAUER

Keyword(s):

Numerical Realization ◽

Discontinuous Solutions ◽

Moving Grids ◽

Ill Posed ◽

Surface Representations

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REGULARIZATION FOR SURFACE REPRESENTATIONS OF DISCONTINUOUS SOLUTIONS OF LINEAR ILL-POSED PROBLEMS

Numerical Functional Analysis and Optimization ◽

10.1081/nfa-100103789 ◽

2001 ◽

Vol 22 (1-2) ◽

pp. 79-105 ◽

Author(s):

Stefan Kindermann ◽

Andreas Neubauer

Keyword(s):

Discontinuous Solutions ◽

Ill Posed ◽

Surface Representations

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Computation of discontinuous solutions of 2D linear ill-posed integral equations via adaptive grid regularization

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip.2007.005 ◽

2007 ◽

Vol 15 (1) ◽

pp. 99-106 ◽

Author(s):

A. Neubauer

Keyword(s):

Integral Equations ◽

Adaptive Grid ◽

Discontinuous Solutions ◽

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Application of functions of several variables with limited variations for piecewise uniform regularization of ill-posed problems

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip.1998.6.1.67 ◽

1998 ◽

Vol 6 (1) ◽

Author(s):

A. S. LEONOV

Keyword(s):

Several Variables ◽

Ill Posed ◽

Uniform Regularization

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Regularization for Curve Representations: Uniform Convergence for Discontinuous Solutions of Ill-Posed Problems

SIAM Journal on Applied Mathematics ◽

10.1137/s0036139997321451 ◽

1998 ◽

Vol 58 (6) ◽

pp. 1891-1900 ◽

Author(s):

Andreas Neubauer ◽

Otmar Scherzer

Keyword(s):

Uniform Convergence ◽

Discontinuous Solutions ◽

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Numerical piecewise-uniform regularization for two-dimensional ill-posed problems

Inverse Problems ◽

10.1088/0266-5611/15/5/304 ◽

1999 ◽

Vol 15 (5) ◽

pp. 1165-1176 ◽

Author(s):

A S Leonov

Keyword(s):

Two Dimensional ◽

Ill Posed ◽

Uniform Regularization

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On multidimensional ill-posed problems with discontinuous solutions

Siberian Mathematical Journal ◽

10.1007/bf02732361 ◽

1998 ◽

Vol 39 (1) ◽

pp. 63-73 ◽

Author(s):

A. S. Leonov

Keyword(s):

Discontinuous Solutions ◽

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Estimation of discontinuous solutions of ill-posed problems via adaptive grid regularization

Journal of Inverse and Ill-Posed Problems ◽

10.1515/156939406779801960 ◽

2006 ◽

Vol 14 (7) ◽

pp. 705-716 ◽

Author(s):

A. Neubauer

Keyword(s):

Adaptive Grid ◽

Discontinuous Solutions ◽

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