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Regularization results for inhomogeneous ill-posed problems in Banach space. (English) Zbl 07908114

Deines, Alyson (ed.) et al., Advances in the mathematical sciences. AWM research symposium, Los Angeles, CA, USA, April 8–9, 2017. Cham: Springer. Assoc. Women Math. Ser. 15, 233-244 (2018).

MSC: 65J20 34G10

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Ugulava, Duglas; Zarnadze, David

Ill-posed problems and associated with them spaces of orbits and orbital operators. (English) Zbl 1513.47028

Rep. Enlarged Sess. Semin. I. Vekua Inst. Appl. Math. 32, 79-82 (2018).

MSC: 47A52

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Cao, Jianbing; Jiao, Hongwei

Perturbation bounds for the metric projection of a point onto a linear manifold in reflexive strictly convex Banach spaces. (English) Zbl 1497.47023

Filomat 32, No. 19, 6829-6836 (2018).

MSC: 47A55 46B20 47A52

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Yang, Fan; Zhang, Yan; Li, Xiao-Xiao; Huang, Can-Yun

The quasi-boundary value regularization method for identifying the initial value with discrete random noise. (English) Zbl 1499.35709

Bound. Value Probl. 2018, Paper No. 108, 12 p. (2018).

MSC: 35R25 47A52 35R30

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Feng, Xiaoli; Qian, Zhi

An a posteriori wavelet method for solving two kinds of ill-posed problems. (English) Zbl 1499.42156

Int. J. Comput. Math. 95, No. 9, 1893-1909 (2018).

MSC: 42C40 47A52 65J20 65T60

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Zhang, Aixia; Gu, Yan; Hua, Qingsong; Chen, Wen

A regularized singular boundary method for inverse Cauchy problem in three-dimensional elastostatics. (English) Zbl 1488.65590

Adv. Appl. Math. Mech. 10, No. 6, 1459-1477 (2018).

MSC: 65N21 65N80 74B10 65N35 65J20 60H50

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Fayazov, K. S.; Xudayberganov, Y. K.

Ill-posed boundary value problem for a mixed type equation with two degenerate lines. (English) Zbl 1474.65325

Uzb. Math. J. 2018, No. 2, 32-42 (2018).

MSC: 65M30 47A52 35R25 35K65

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Foadian, Saedeh; Pourgholi, Reza; Hashem Tabasi, S.

Cubic B-spline method for the solution of an inverse parabolic system. (English) Zbl 1466.65103

Appl. Anal. 97, No. 3, 438-465 (2018).

MSC: 65M32 65M30 65M70 65J20 65F22 65M20 65D07 35G46 35R25

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Furuya, Kiyoko

On “well posed function spaces” for \(L^2\)-illposed hyperbolic equations. (English) Zbl 1456.47013

J. Nonlinear Convex Anal. 19, No. 9, 1525-1530 (2018).

MSC: 47D06 35M13 35R25

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Buccini, Alessandro; Park, Yonggi; Reichel, Lothar

Numerical aspects of the nonstationary modified linearized Bregman algorithm. (English) Zbl 1427.65052

Appl. Math. Comput. 337, 386-398 (2018).

MSC: 65F22 65F10 65R32 65F08

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Reddy, G. M. M.; Vynnycky, M.; Cuminato, J. A.

On efficient reconstruction of boundary data with optimal placement of the source points in the MFS: application to inverse Stefan problems. (English) Zbl 1428.65053

Inverse Probl. Sci. Eng. 26, No. 9, 1249-1279 (2018).

MSC: 65M70 65K10 65M32 65M30 80A22 80A23 35R35 65M80 65F22 65F05 35Q79

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Eksioglu, Ender M.; Tanc, A. Korhan

Denoising AMP for MRI reconstruction: BM3D-AMP-MRI. (English) Zbl 1478.94034

SIAM J. Imaging Sci. 11, No. 3, 2090-2109 (2018).

MSC: 94A08 47A52 49M99 65J22

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Wang, Zhengsheng; Mu, Liming; Liu, Rongrong; Xu, Guili

Arnoldi projection fractional Tikhonov for large scale ill-posed problems. (English) Zbl 1424.65046

Trans. Nanjing Univ. Aeronaut. Astronaut. 35, No. 3, 395-402 (2018).

MSC: 65F22

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Katta, Ravinder; Reddy, G. D.; Sukavanam, N.

Computation of control for linear approximately controllable system using weighted Tikhonov regularization. (English) Zbl 1426.93027

Appl. Math. Comput. 317, 252-263 (2018).

MSC: 93B05 47A52 65J10 93C25

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Mahale, Pallavi; Dadsena, Pradeep Kumar

Simplified generalized Gauss-Newton method for nonlinear ill-posed operator equations in Hilbert scales. (English) Zbl 1460.47029

Comput. Methods Appl. Math. 18, No. 4, 687-702 (2018).

MSC: 47J06 65F22 65J15 65J22 65M30

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Karl, Veronika; Pörner, Frank

A joint Tikhonov regularization and augmented Lagrange approach for ill-posed state constrained control problems with sparse controls. (English) Zbl 1414.49034

Numer. Funct. Anal. Optim. 39, No. 14, 1543-1573 (2018).

MSC: 49M20 65K10 90C30 49N10

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Al-Jamal, Mohammad F.; Alomari, A. K.; Gockenbach, Mark S.

Smoothing via elliptic operators with application to edge detection. (English) Zbl 07039137

Inverse Probl. Sci. Eng. 26, No. 5, 657-676 (2018).

MSC: 65D25 65F22 47A52 35J05

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Freeden, Willi; Nashed, M. Zuhair

Ill-posed problems: operator methodologies of resolution and regularization. (English) Zbl 1464.47007

Freeden, Willi (ed.) et al., Handbook of mathematical geodesy. Functional analytic and potential theoretic methods. Cham: Birkhäuser. Geosyst. Math., 201-314 (2018).

Reviewer: Bernd Hofmann (Chemnitz)

MSC: 47A52 35R30 65J20 86A30 65N21 86-02

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Belov, A. A.; Kalitkin, N. N.

Solution of the Fredholm equation of the first kind by mesh method with Tikhonov regularization. (Russian. English summary) Zbl 1424.45003

Mat. Model. 30, No. 8, 67-88 (2018).

Reviewer: Sergei Georgievich Zhuravlev (Moskva)

MSC: 45B05 45A05 65R30 85A15

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Yang, Hao; Qiu, Hang; Chen, Leiting

An optimized direction statistics for detecting and removing random-valued impulse noise. (English) Zbl 1412.94012

J. Ind. Manag. Optim. 14, No. 2, 597-611 (2018).

MSC: 94A08 47A52

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Niebsch, Jenny; Ramlau, Ronny

Frequency-dependent reconstruction of imbalances. (English) Zbl 1408.65083

ETNA, Electron. Trans. Numer. Anal. 48, 435-449 (2018).

MSC: 65N21 47A52 15A18 65F20 35R30 65R20 65L09 74H20 35Q74

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Cui, Jing-Jing; Peng, Guo-Hua; Lu, Quan; Huang, Zheng-Ge

Accelerated GNHSS iterative method for weighted Toeplitz regularized least-squares problems from image restoration. (English) Zbl 1413.65056

Comput. Appl. Math. 37, No. 5, 6152-6175 (2018).

MSC: 65F10 15B05 65F50 65N20

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Shen, Li; Quinto, Eric Todd; Wang, Shiqiang; Jiang, Ming

Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography. (English) Zbl 1408.94590

Inverse Probl. Imaging 12, No. 6, 1343-1364 (2018).

MSC: 94A08 15A29 47A52 68U10

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Li, Qin; Shu, Ruiwen; Wang, Li

A new numerical approach to inverse transport equation with error analysis. (English) Zbl 1450.65139

SIAM J. Numer. Anal. 56, No. 6, 3358-3385 (2018).

MSC: 65N20 65N21 65R20 65R32 65K10 35F15 35R09 45K05 35R30

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Beilina, Larisa; Guillot, Genevieve; Niinimäki, Kati

On finite element method for magnetic resonance imaging. (English) Zbl 1402.78024

Beilina, L. (ed.) et al., Nonlinear and inverse problems in electromagnetics, PIERS 2017, St. Petersburg, Russia, May 22–25, 2017. Cham: Springer (ISBN 978-3-319-94059-5/hbk; 978-3-319-94060-1/ebook). Springer Proceedings in Mathematics & Statistics 243, 119-132 (2018).

MSC: 78M10 45B05 78M50 45Q05 65R20 65R30 65F22

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Borges, Leonardo S.; Bazán, Fermín S. V.; Bedin, Luciano

A projection-based algorithm for \(\ell_{2}\)-\(\ell_{p}\) Tikhonov regularization. (English) Zbl 1405.65056

Math. Methods Appl. Sci. 41, No. 15, 5919-5938 (2018).

Reviewer: Constantin Popa (Constanţa)

MSC: 65F22

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Machado, M. P.; Margotti, Fábio; Leitão, Antonio

On nonstationary iterated Tikhonov methods for ill-posed equations in Banach spaces. (English) Zbl 1471.47008

Hofmann, Bernd (ed.) et al., New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 – November 3, 2017. Cham: Birkhäuser. Trends Math., 175-193 (2018).

Reviewer: Regina Sandra Burachik (Adelaide)

MSC: 47A52 65F22

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Hämarik, Uno; Kangro, Urve

On self-regularization of ill-posed problems in Banach spaces by projection methods. (English) Zbl 06976713

Hofmann, Bernd (ed.) et al., New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 – November 3, 2017. Cham: Birkhäuser. Trends Math., 89-105 (2018).

MSC: 47A52

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Gerth, Daniel; Hofmann, Bernd

On \(\ell^1\)-regularization under continuity of the forward operator in weaker topologies. (English) Zbl 06976712

Hofmann, Bernd (ed.) et al., New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 – November 3, 2017. Cham: Birkhäuser. Trends Math., 67-88 (2018).

MSC: 47A52

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Clason, Christian; Do, Thi Bich Tram

Convex regularization of discrete-valued inverse problems. (English) Zbl 06976710

Hofmann, Bernd (ed.) et al., New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 – November 3, 2017. Cham: Birkhäuser. Trends Math., 31-51 (2018).

MSC: 47A52 65-XX