Výsledky vyhledávání - 65J20 Numerical solutions of ill-posed problems in abstract spaces

SCHRÖDINGERIZATION BASED COMPUTATIONALLY STABLE ALGORITHMS FOR ILL-POSED PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS.

Autoři: SHI JIN NANA LIU CHUWEN MA

Zdroj: SIAM Journal on Scientific Computing; 2025, Vol. 47 Issue 4, pB976-B1000, 25p

Témata: PARTIAL differential equations, QUANTUM computing, NUMERICAL solutions to equations, ERROR analysis in mathematics, HAMILTONIAN operator, HAMILTONIAN systems

A class of regularization schemes for linear ill-posed problems in Banach spaces under low order source conditions

Autoři: Plato, Robert

Témata: Numerical Analysis, 65J20 65J22 47D06 26A33

Relation: http://arxiv.org/abs/2509.05418

Dostupnost: http://arxiv.org/abs/2509.05418

On iterative methods for solving ill-posed problems modeled by partial differential equations

Autoři: J. Baumeister Antonio Leitão

Zdroj: jiip. 9:13-29

Témata: ill-posed problems, regularization, Numerical solutions of ill-posed problems in abstract spaces, partial differential equations, FOS: Mathematics, iterative methods, Ill-posed problems for PDEs, spectral theory, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences, 65J20, 47A52

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/pdf/2011.14441
http://arxiv.org/abs/2011.14441
https://zbmath.org/1618298
https://doi.org/10.1515/jiip.2001.9.1.13
https://dblp.uni-trier.de/db/journals/corr/corr2011.html#abs-2011-14441
https://uk.arxiv.org/abs/2011.14441
https://arxiv.org/abs/2011.14441
https://arxiv.org/pdf/2011.14441v1
http://export.arxiv.org/pdf/2011.14441
http://ui.adsabs.harvard.edu/abs/2020arXiv201114441B/abstract
https://www.degruyter.com/view/journals/jiip/9/1/article-p13.xml?language=en

Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems

Autoři: Bruckner, Gottfried Pereverzev, Sergei V.

Zdroj: Inverse Problems. 19:147-156

Témata: ddc:510, self-regularization, 65J20, numerical examples, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, severely ill-posed problems, regularization by discretization, article, Hilbert space, 65R30, error bounds, integral equation of the first kind, 01 natural sciences, generalized inverse, severely ill-posed problems -- regularization by discretization -- projection methods -- integral equation of the first kind, Linear ill-posed problems, linear injective compact operator, a posteriori parameter choice strategies, Numerical solutions to equations with linear operators, projection methods, 0101 mathematics

Popis souboru: application/xml

Přístupová URL adresa: https://internal.iopscience.iop.org/article/10.1088/0266-5611/19/1/308
https://iopscience.iop.org/article/10.1088/0266-5611/19/1/308
http://ui.adsabs.harvard.edu/abs/2003InvPr..19..147B/abstract

Stable Approximations of a Minimal Surface Problem with Variational Inequalities: Stable approximations of a minimal surface problem with variational inequalities

Autoři: Nashed, M. Zuhair Scherzer, Otmar

Zdroj: Abstract and Applied Analysis, Vol 2, Iss 1-2, Pp 137-161 (1997)
Abstr. Appl. Anal. 2, no. 1-2 (1997), 137-161

Témata: 65J20, Numerical optimization and variational techniques, nondifferentiable optimization in nonreflexive spaces, Numerical solutions of ill-posed problems in abstract spaces, regularization, 01 natural sciences, QA1-939, Minimal surfaces and optimization, Regularity of solutions in optimal control, bounded variation, 49J45, Uzawa′s algorithm, 0101 mathematics, 49N60, 49J40, 26A45, 65K10, Methods involving semicontinuity and convergence, relaxation, Numerical solutions to equations with nonlinear operators, 65J15, Functions of bounded variation, generalizations, Variational inequalities, 49Q05, relaxed Dirichlet problem, Minimal surface problem, minimal surface problem, bounded variation norm, Uzawa's algorithm, Mathematics, variational inequalities

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: https://downloads.hindawi.com/journals/aaa/1997/383457.pdf
https://zbmath.org/1370675
https://doi.org/10.1155/s1085337597000316
https://doaj.org/article/3fd1a50cf78a4426a17f737e3a92078c
https://projecteuclid.org/journals/abstract-and-applied-analysis/volume-2/issue-1-2/Stable-approximations-of-a-minimal-surface-problem-with-variational-inequalities/10.1155/S1085337597000316.short
https://www.emis.de/journals/HOA/AAA/Volume2_1-2/161.pdf
https://downloads.hindawi.com/journals/aaa/1997/383457.pdf
https://www.hindawi.com/journals/aaa/1997/383457/
http://emis.library.cornell.edu/journals/HOA/AAA/Volume2_1-2/161.pdf
http://ui.adsabs.harvard.edu/abs/1997AbApA...2..137N/abstract
http://projecteuclid.org/euclid.aaa/1049737247

ULTRA-WEAK LEAST SQUARES DISCRETIZATIONS FOR UNIQUE CONTINUATION AND CAUCHY PROBLEMS.

Autoři: MONSUUR, HARALD STEVENSON, ROB

Zdroj: SIAM Journal on Numerical Analysis; 2025, Vol. 63 Issue 3, p1344-1368, 25p

Témata: CAUCHY problem, POISSON'S equation, MEASUREMENT uncertainty (Statistics), VARIATIONAL approach (Mathematics), LEAST squares, CONTINUATION methods, NUMERICAL solutions to equations

Some comments on Wicksell's problem

Autoři: University of Florida, USA ( host institution ) Mair, Bernard A. Ruymgaart, Frits H. a další

Zdroj: Journal of Statistical Planning and Inference. 87:31-42

Témata: Density estimation, Inverse estimation, Numerical solutions of ill-posed problems in abstract spaces, regularization, Asymptotic efficiency, primary 62G07, Unfolding, Integrated mean square error, 0101 mathematics, 01 natural sciences, Regularized inverse, secondary 65J20

Popis souboru: application/xml; [Elsevier APIv3]

Přístupová URL adresa: https://www.sciencedirect.com/science/article/pii/S0378375899001780

Arcangeli′s type discrepancy principles for a class of regularization methods using a modified projection scheme: Arcangeli's type discrepancy principles for a class of regularization methods using a modified projection scheme

Autoři: Nair, M. T. Rajan, M. P.

Zdroj: Abstract and Applied Analysis, Vol 6, Iss 6, Pp 339-355 (2001)
Abstr. Appl. Anal. 6, no. 6 (2001), 339-355

Témata: 65J20, linear integral equation of the first kind, 65J10, parameter choice, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Fredholm integral equations, Numerical methods for integral equations, Arcangeli-type discrepancy principle, Tikhonov's method, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, numerical example, regularization methods, Numerical solutions to equations with linear operators, 0103 physical sciences, QA1-939, projection methods, linear ill-posed problems, 47L10, 0101 mathematics, Mathematics

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: http://downloads.hindawi.com/journals/aaa/2001/572989.pdf
https://zbmath.org/1750371
https://doi.org/10.1155/s1085337501000653
https://doaj.org/article/078587ef12374d8483b16b86c0ccbbbf
http://emis.maths.adelaide.edu.au/journals/HOA/AAA/Volume6_6/355.pdf
https://projecteuclid.org/download/pdfview_1/euclid.aaa/1050266895
http://www.emis.de/journals/HOA/AAA/Volume6_6/355.pdf
https://downloads.hindawi.com/journals/aaa/2001/572989.pdf
https://eudml.org/doc/49771
https://www.hindawi.com/journals/aaa/2001/572989/
https://projecteuclid.org/euclid.aaa/1050266895

On a new notion of regularizer: On a new notion of regularizer.

Autoři: Alexander G. Ramm

Zdroj: Journal of Physics A: Mathematical and General. 36:2191-2195

Témata: Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical solutions to equations with nonlinear operators, nonlinear operator equation, Nonlinear ill-posed problems, regularizer, ill-posed problem, Numerical Analysis (math.NA), 01 natural sciences, numerical example, Banach spaces, 47A52, 65F22, 65J20, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/pdf/math/0301379
http://arxiv.org/abs/math/0301379
https://zbmath.org/2071967
https://doi.org/10.1088/0305-4470/36/8/315
https://arxiv.org/pdf/math/0301379
http://core.ac.uk/display/2570223
https://arxiv.org/abs/math/0301379
http://ui.adsabs.harvard.edu/abs/2003JPhA...36.2191R/abstract
https://inis.iaea.org/Search/search.aspx?orig_q=RN:34048044
https://www.math.ksu.edu/~ramm/papers/444j.pdf
http://www.math.ksu.edu/~ramm/papers/444j.pdf
http://iopscience.iop.org/article/10.1088/0305-4470/36/8/315

Applications of the Backus-Gilbert method to linear and some nonlinear equations

Autoři: Antonio Leitão

Zdroj: Inverse Problems. 14:1285-1297

Témata: Inverse problems for PDEs, Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical solutions to equations with nonlinear operators, Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs, Numerical Analysis (math.NA), 01 natural sciences, Fréchet differentiable operators, noisy data, Green formula, Iterative procedures involving nonlinear operators, error estimates, Backus-Gilbert method, FOS: Mathematics, Mathematics - Numerical Analysis, nonlinear systems, 65J20, 47A52, 0105 earth and related environmental sciences

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/pdf/2011.14407
http://arxiv.org/abs/2011.14407
https://arxiv.org/pdf/2011.14407v1
https://arxiv.org/abs/2011.14407
http://iopscience.iop.org/article/10.1088/0266-5611/14/5/012/pdf
https://iopscience.iop.org/article/10.1088/0266-5611/14/5/012/pdf
https://ui.adsabs.harvard.edu/abs/1998InvPr..14.1285L/abstract
http://iopscience.iop.org/0266-5611/14/5/012
http://mtm.ufsc.br/~aleitao/public/reprints/pap1998-l-IP.pdf
https://dblp.uni-trier.de/db/journals/corr/corr2011.html#abs-2011-14407

Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections.

Autoři: Flemming, Jens

Zdroj: Applicable Analysis; May2012, Vol. 91 Issue 5, p1029-1044, 16p

Témata: SMOOTHNESS of functions, HILBERT space, NUMERICAL solutions to differential equations, OPERATOR theory, MATHEMATICAL inequalities, BOUNDARY value problems, APPROXIMATION theory, HOMOTOPY equivalences

On a class of finite difference methods for ill-posed Cauchy problems with noisy data.

Autoři: Bakushinsky, Anatoly B. Kokurin, Mikhail Yu. Kokurin, Mikhail M.

Zdroj: Journal of Inverse & Ill-Posed Problems; Feb2011, Vol. 18 Issue 9, p959-977, 19p

Témata: NUMERICAL solutions to the Cauchy problem, NUMERICAL solutions to linear differential equations, FINITE differences, APPROXIMATION theory, LINEAR operators, HILBERT space, ERROR analysis in mathematics

Regularization with Optimal Space-Time Priors.

Autoři: Bubba, Tatiana A. Heikkilä, Tommi Labate, Demetrio a další

Zdroj: SIAM Journal on Imaging Sciences; 2025, Vol. 18 Issue 3, p1563-1600, 38p

An Adaptive Heavy Ball Method for Ill-Posed Inverse Problems.

Autoři: Qinian Jin Qin Huang

Zdroj: SIAM Journal on Imaging Sciences; 2024, Vol. 17 Issue 4, p2212-2241, 30p

On the relation between constraint regularization, level sets and shape optimization: On the relation between constraint regularization, level sets, and shape optimization

Autoři: Otmar Scherzer Antonio Leitão

Zdroj: Inverse Problems. 22:1507-1507

Témata: 65J20, 47J06, Numerical solutions of ill-posed problems in abstract spaces, regularization, inverse problems, Numerical solutions to equations with nonlinear operators, Tikhonov regularization, asymptotic regularization, Nonlinear ill-posed problems, Numerical Analysis (math.NA), ill-posed problems, Optimization and Control (math.OC), shape optimization, FOS: Mathematics, level set methods, Mathematics - Numerical Analysis, Mathematics - Optimization and Control

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/pdf/2011.07178
http://arxiv.org/abs/2011.07178
https://zbmath.org/1916682
https://doi.org/10.1088/0266-5611/19/1/101
https://ui.adsabs.harvard.edu/abs/2003InvPr..19L...1L/abstract
https://arxiv.org/pdf/2011.07178v1
https://arxiv.org/abs/2011.07178
https://dblp.uni-trier.de/db/journals/corr/corr2011.html#abs-2011-07178
https://arxiv.org/abs/2011.07178
http://www.mat.unimi.it/users/cecilia/gargnano2003/abstracts/scherzer.pdf
https://arxiv.org/pdf/2011.07178
http://ui.adsabs.harvard.edu/abs/2006InvPr..22.1507L/abstract
http://mtm.ufsc.br/~aleitao/public/reprints/pap2003-ls-IP.pdf

Randomized block coordinate descent method for linear ill-posed problems

Autoři: Qinian Jin Duo Liu

Zdroj: Inverse Problems. 41:035012

Témata: convergence, Numerical analysis in abstract spaces, Mathematical programming, imaging, 65J20, 65J22, 65J10, 94A08, Numerical Analysis (math.NA), Optimization and Control (math.OC), Numerical methods for mathematical programming, optimization and variational techniques, FOS: Mathematics, linear ill-posed problems, Mathematics - Numerical Analysis, randomized block coordinate descent method, convex regularization term, Mathematics - Optimization and Control

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2405.13340

On sequential minimization of Tikhonov functionals in ill-posed problems with a priori information on solutions.

Autoři: Kokurin, Mikhail Yu.

Zdroj: Journal of Inverse & Ill-Posed Problems; Feb2011, Vol. 18 Issue 9, p1031-1050, 20p

Témata: NUMERICAL solutions to nonlinear operator equations, ITERATIVE methods (Mathematics), HILBERT space, FUNCTIONALS, APPROXIMATION theory, MATHEMATICAL optimization, MATHEMATICAL sequences

On the Convergence of a Data-Driven Regularized Stochastic Gradient Descent for Nonlinear Ill-Posed Problems.

Autoři: Zehui Zhou

Zdroj: SIAM Journal on Imaging Sciences; 2025, Vol. 18 Issue 1, p388-448, 61p

Higher order convergence rates for Bregman iterated variational regularization of inverse problems

Autoři: Sprung, Benjamin Hohage, Thorsten

Přispěvatelé: Sprung, Benjamin Hohage, Thorsten

Zdroj: Numerische Mathematik. 141:215-252

Témata: 65J20, 65J22, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences

Přístupová URL adresa: http://arxiv.org/pdf/1710.09244
http://arxiv.org/abs/1710.09244
https://link.springer.com/article/10.1007/s00211-018-0987-x
https://dblp.uni-trier.de/db/journals/nm/nm141.html#SprungH19
https://doi.org/10.1007/s00211-018-0987-x
http://ui.adsabs.harvard.edu/abs/2017arXiv171009244S/abstract
https://arxiv.org/abs/1710.09244
https://arxiv.org/pdf/1710.09244.pdf
https://resolver.sub.uni-goettingen.de/purl?gro-2/68640

An extension of the variational inequality approach for nonlinear ill-posed problems

Autoři: Bot, Radu Ioan Hofmann, Bernd

Témata: 65J20, 47J06, 47A52, 49N45, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences

Přístupová URL adresa: http://arxiv.org/abs/0909.5093