A two-parameter Tikhonov regularization for a fractional sideways problem with two interior temperature measurements

Συγγραφείς: Dang Duc Trong, Dinh Nguyen Duy Hai, Nguyen Dang Minh, Nguyen Nhu Lan

Πηγή: Mathematics and Computers in Simulation. 229:491-511

Θεματικοί όροι: fractional order equation, Linear operators and ill-posed problems, regularization, Error bounds for boundary value problems involving PDEs, Ill-posed problems for PDEs, ill-posed problem, Tikhonov regularization method, Fractional partial differential equations, optimal convergence estimates

Περιγραφή αρχείου: application/xml

Solution of linear ill-posed operator equations by modified truncated singular value expansion

Συγγραφείς: Laura Dykes, Mykhailo Kuian, Thomas Mach, Silvia Noschese, Lothar Reichel

Πηγή: Journal of Computational and Applied Mathematics. 467:116621

Θεματικοί όροι: regularization, truncated singular value expansion, Numerical solutions of ill-posed problems in abstract spaces, Linear operators and ill-posed problems, regularization, Numerical solutions to equations with linear operators, ill-posed problem, Chebfun

Περιγραφή αρχείου: application/xml; application/pdf

Fourier regularization for solving sideways problem of a nonlinear time-fractional diffusion equation

Συγγραφείς: Wu, Hanghang, Yang, Hongqi

Πηγή: Computational and Applied Mathematics. 44

Θεματικοί όροι: Inverse problems for PDEs, sideways problem, Linear operators and ill-posed problems, regularization, Ill-posed problems for PDEs, Fourier regularization, error estimate, nonlinear time-fractional diffusion equation, a posteriori parameter choice

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/8034169
https://doi.org/10.1007/s40314-025-03124-y

Norms in sinogram space and stability estimates for the Radon transform

Συγγραφείς: Stefan Kindermann, Simon Hubmer

Πηγή: Inverse Problems. 41:025008

Θεματικοί όροι: Mathematics - Functional Analysis, inverse and ill-posed problems, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, stability estimates, FOS: Mathematics, Radon transform, total variation regularization, Functional Analysis (math.FA)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2403.07466

The modified quasi-boundary-value method for an ill-posed generalized elliptic problem

Συγγραφείς: Selmani Wissame, Boussetila Nadjib, Kirane Mokhtar, Alsulami Hamed

Πηγή: Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 32-36 (2024)

Θεματικοί όροι: QA299.6-433, fractional elliptic equations, Linear operators and ill-posed problems, regularization, Numerical solutions of ill-posed problems in abstract spaces, regularization, Fractional ordinary differential equations, quasi-boundary-value method, ill-posed problems, 35r11, 35r30, Linear differential equations in abstract spaces, 35j25, 47a52, 35r25, Analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://doaj.org/article/ca315cf7326b4cb1b3ed9bdf27da55ed

RECOVERY OF THE TEMPERATURE DISTRIBUTION IN A MULTILAYER FRACTIONAL DIFFUSION EQUATION: Recovery of the temperature distribution in a multilayer fractional diffusion equation

Συγγραφείς: KHIEU T. TRAN, LUAN N. TRAN, HONG B. Q. NGUYEN, KHANH Q. TRA

Πηγή: Bulletin of the Australian Mathematical Society. 100:344-352

Θεματικοί όροι: fractional diffusion equation, Linear operators and ill-posed problems, regularization, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, ill-posed problem, 0101 mathematics, composite material, Fourier spectral method, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/recovery-of-the-temperature-distribution-in-a-multilayer-fractional-diffusion-equation/05C132208A9E6366AF2517FDB1C253CE
https://dialnet.unirioja.es/servlet/articulo?codigo=7167305
https://journal.austms.org.au/ojs/index.php/Bulletin/article/view/13753

Convergence of non-linear diagonal frame filtering for regularizing inverse problems

Συγγραφείς: Andrea Ebner, Markus Haltmeier

Πηγή: Inverse Problems. 40:055009

Θεματικοί όροι: Signal theory (characterization, reconstruction, filtering, etc.), Linear operators and ill-posed problems, regularization, Numerical solutions of ill-posed problems in abstract spaces, regularization, Tikhonov regularization, Hilbert space, singular value decomposition, linear inverse problem, Numerical solution to inverse problems in abstract spaces, General harmonic expansions, frames, Numerical Analysis (math.NA), 01 natural sciences, Bregman distance, diagonal frame decomposition, FOS: Mathematics, plug-and-play regularization, Mathematics - Numerical Analysis, 0101 mathematics, non-linear frame-based filtering

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2308.15666

Runge–Kutta integrators yield optimal regularization schemes: Runge-Kutta integrators yield optimal regularization schemes

Συγγραφείς: Rieder, A.

Πηγή: Inverse Problems, 21 (2), 453-471

Θεματικοί όροι: ddc:510, numerical examples, convergence, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Showalter's method, Tikhonov regularization, Hilbert space, asymptotic regularization, implicit Euler scheme, 01 natural sciences, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Linear differential equations in abstract spaces, Numerical solutions to equations with linear operators, evolution equation, linear ill-posed problems, 0101 mathematics, Runge-Kutta integrators, order optimality, Mathematics

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://publikationen.bibliothek.kit.edu/1000011042/762671
https://zbmath.org/2174678
https://doi.org/10.1088/0266-5611/21/2/003
http://digbib.ubka.uni-karlsruhe.de/volltexte/documents/762671
http://ui.adsabs.harvard.edu/abs/2005InvPr..21..453R/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/21/2/003
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-110850
https://publikationen.bibliothek.kit.edu/1000011085/772258
https://doi.org/10.5445/IR/1000011085
https://publikationen.bibliothek.kit.edu/1000011085
http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:swb:90-110428
https://doi.org/10.5445/IR/1000011042
https://publikationen.bibliothek.kit.edu/1000011042
https://publikationen.bibliothek.kit.edu/1000011042/762671

Regularizing algorithms for detecting discontinuities in ill-posed problems

Συγγραφείς: T. V. Antonova, A. L. Ageev

Πηγή: Computational Mathematics and Mathematical Physics. 48:1284-1292

Θεματικοί όροι: Linear operators and ill-posed problems, regularization, noisy function, 0102 computer and information sciences, 0101 mathematics, singularities, regularizing algorithms, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/article/10.1134/S0965542508080034
https://ui.adsabs.harvard.edu/abs/2008CMMPh..48.1284A/abstract

Duality-based regularization in a linear convex mathematical programming problem

Συγγραφείς: M. I. Sumin

Πηγή: Computational Mathematics and Mathematical Physics. 47:579-600

Θεματικοί όροι: Linear operators and ill-posed problems, regularization, regularization algorithm, stopping rule, duality, Optimality conditions for problems involving partial differential equations, linearly convex problem, dual iteration regularization, 0101 mathematics, 01 natural sciences, mathematical programming

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/5200945
https://doi.org/10.1134/s0965542507040045
https://ui.adsabs.harvard.edu/abs/2007CMMPh..47..579S/abstract
https://link.springer.com/article/10.1134/S0965542507040045
https://link.springer.com/content/pdf/10.1134/S0965542507040045.pdf

A new discrepancy principle

Συγγραφείς: Alexander G. Ramm

Πηγή: Journal of Mathematical Analysis and Applications. 310:342-345

Θεματικοί όροι: 47H15, 45G10,35B25, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Applied Mathematics, discrepancy principle, Hilbert space, Numerical Analysis (math.NA), minimal-norm solution, 01 natural sciences, ill-posed problems, Numerical solutions to equations with linear operators, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/math/0408191
https://zbmath.org/2207275
https://doi.org/10.1016/j.jmaa.2005.01.062
https://core.ac.uk/display/21861235
https://arxiv.org/pdf/math/0408191
https://www.sciencedirect.com/science/article/pii/S0022247X05000910
https://www.math.ksu.edu/~ramm/papers/480j.pdf
http://www.math.ksu.edu/~ramm/papers/480j.pdf
http://ui.adsabs.harvard.edu/abs/2005JMAA..310..342R/abstract

Preconditioning Landweber iteration in Hilbert scales

Συγγραφείς: Herbert Egger, Andreas Neubauer

Πηγή: Numerische Mathematik. 101:643-662

Θεματικοί όροι: Landweber iteration, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, preconditioning, Numerical solutions to equations with nonlinear operators, Numerical solutions to equations with linear operators, Nonlinear ill-posed problems, Numerical solution to inverse problems in abstract spaces, numerical results, 0101 mathematics, ill-posed inverse problems, Hilbert scales, 01 natural sciences

Περιγραφή αρχείου: application/xml

On a quasi-optimal regularized projection method for solving operator equations of the first kind

Συγγραφείς: S. G. Solodky

Πηγή: Inverse Problems. 21:1473-1485

Θεματικοί όροι: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, Hilbert space, discrepancy principle, ill-posed problem, Showalter method, 01 natural sciences, Numerical methods for ill-posed problems for integral equations, Tikhonov method, regularization methods, compact linear operator, Numerical solutions to equations with linear operators, optimal order of accuracy, 0101 mathematics, linear operator equation, regularized projection method algorithm

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2215125
https://doi.org/10.1088/0266-5611/21/4/017
https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1473S/abstract
http://iopscience.iop.org/article/10.1088/0266-5611/21/4/017/pdf

Regularization of ill-posed problems in Banach spaces: convergence rates

Συγγραφείς: Elena Resmerita

Πηγή: Inverse Problems. 21:1303-1314

Θεματικοί όροι: ill-posed problems, regularization, linear bounded compact operator, convergence, Numerical solutions of ill-posed problems in abstract spaces, Linear operators and ill-posed problems, regularization, Numerical solutions to equations with linear operators, Hilbert space, 0101 mathematics, 01 natural sciences, Bregman distance, entropic regularization, total variation regularization

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1303R/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/21/4/007/meta

All solutions of system of ill-posed operator equations of the first kind

Συγγραφείς: Minggen Cui, Zhong Chen

Πηγή: Applied Mathematics and Computation. 165:749-758

Θεματικοί όροι: analytic solutions, Linear operators and ill-posed problems, regularization, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), ill-posed operator equation, 0101 mathematics, reproducing kernel Hilbert space, 01 natural sciences, Equations and inequalities involving linear operators, with vector unknowns

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://dblp.uni-trier.de/db/journals/amc/amc165.html#CuiC05
https://www.sciencedirect.com/science/article/pii/S0096300304004151
https://doi.org/10.1016/j.amc.2004.04.040

Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

Συγγραφείς: Freitag, Melina A, Hofmann, B

Πηγή: Freitag, M A & Hofmann, B 2005, 'Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems', Journal of Inverse and Ill-posed Problems, vol. 13, no. 2, pp. 123-148. https://doi.org/10.1515/1569394053978524

Θεματικοί όροι: Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, Tikhonov regularization, name=Applied Mathematics, Numerical solution to inverse problems in abstract spaces, compact operator, ill-posed problem, multiplication operators, 01 natural sciences, Nemytskij operator, linear operator equations, Numerical solutions to equations with linear operators, 0101 mathematics

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://zbmath.org/2204565
https://doi.org/10.1515/1569394053978524
https://purehost.bath.ac.uk/ws/files/141101243/endversion.pdf
https://researchportal.bath.ac.uk/en/publications/analytical-and-numerical-studies-on-the-influence-of-multiplicati
https://core.ac.uk/display/2810776

Regularization for a class of ill-posed Cauchy problems

Συγγραφείς: Quan Zheng, Yongzhong Huang

Πηγή: Proceedings of the American Mathematical Society. 133:3005-3012

Θεματικοί όροι: Linear differential equations in abstract spaces, Linear operators and ill-posed problems, regularization, One-parameter semigroups and linear evolution equations, analytic semigroup, quasi-reversibility, regularizing family, 0101 mathematics, 01 natural sciences, ill-posed Cauchy problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/proc/2005-133-10/S0002-9939-05-07822-6/S0002-9939-05-07822-6.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=1360276
https://www.ams.org/journals/proc/2005-133-10/S0002-9939-05-07822-6/home.html
https://www.ams.org/proc/2005-133-10/S0002-9939-05-07822-6/S0002-9939-05-07822-6.pdf

Convergence rates for Tikhonov regularization based on range inclusions

Συγγραφείς: Bernd Hofmann, Masahiro Yamamoto

Πηγή: Inverse Problems. 21:805-820

Θεματικοί όροι: Hilbert spaces, Inverse problems for PDEs, Tikhonov's regularization method, Numerical solutions of ill-posed problems in abstract spaces, regularization, Linear operators and ill-posed problems, regularization, inverse problems, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, Numerical methods for integral equations, 01 natural sciences, Abel integral equation, Numerical solutions to equations with linear operators, linear ill-posed problems, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.tu-chemnitz.de/mathematik/inverse_probleme/fulltext/inclusion.pdf
https://ui.adsabs.harvard.edu/abs/2005InvPr..21..805H/abstract

Discrepancy principle for the dynamical systems method

Συγγραφείς: Alexander G. Ramm

Πηγή: Communications in Nonlinear Science and Numerical Simulation. 10:95-101

Θεματικοί όροι: ill-posed problems, Linear operators and ill-posed problems, regularization, evolution equations, discrepancy principle, dynamical systems, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://www.math.ksu.edu/~ramm/papers/474.pdf
https://zbmath.org/2107351
https://doi.org/10.1016/s1007-5704(03)00094-7
https://www.sciencedirect.com/science/article/pii/S1007570403000947#!
https://ui.adsabs.harvard.edu/abs/2005CNSNS..10...95R/abstract
https://www.sciencedirect.com/science/article/abs/pii/S1007570403000947

Some results and a conjecture on the degree of ill-posedness for integration operators with weights

Συγγραφείς: Lothar von Wolfersdorf, Bernd Hofmann

Πηγή: Inverse Problems. 21:427-433

Θεματικοί όροι: Linear operators and ill-posed problems, regularization, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://ui.adsabs.harvard.edu/abs/2005InvPr..21..427H/abstract
https://www.tu-chemnitz.de/mathematik/inverse_probleme/fulltext/hofwolf.pdf