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Journal articles on the topic 'Inverse problems'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 August 2024

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1

Coleman, Rodney. "Inverse problems." Journal of Microscopy 153, no. 3 (March 1989): 233–48. http://dx.doi.org/10.1111/j.1365-2818.1989.tb01475.x.

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2

Tanaka, Masa, and A. Kassab. "Inverse problems." Engineering Analysis with Boundary Elements 28, no. 3 (March 2004): 181. http://dx.doi.org/10.1016/s0955-7997(03)00048-1.

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3

Bunge, Mario. "Inverse Problems." Foundations of Science 24, no. 3 (January 10, 2019): 483–525. http://dx.doi.org/10.1007/s10699-018-09577-1.

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4

Romanov, V. G. "SOME GEOMETRIC ASPECTS IN INVERSE PROBLEMS." Eurasian Journal of Mathematical and Computer Applications 3, no. 1 (2015): 68–84. http://dx.doi.org/10.32523/2306-3172-2015-3-4-68-84.

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5

Kabanikhin, S. I., O. I. Krivorotko, D. V. Ermolenko, V. N. Kashtanova, and V. A. Latyshenko. "INVERSE PROBLEMS OF IMMUNOLOGY AND EPIDEMIOLOGY." Eurasian Journal of Mathematical and Computer Applications 5, no. 2 (2017): 14–35. http://dx.doi.org/10.32523/2306-3172-2017-5-2-14-35.

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6

Romanov, V. G. "INVERSE PROBLEMS FOR EQUATIONS WITH A MEMORY." Eurasian Journal of Mathematical and Computer Applications 2, no. 1 (2014): 51–80. http://dx.doi.org/10.32523/2306-3172-2014-2-4-51-80.

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7

Iwamoto, Seiichi, and Takayuki Ueno. "INVERSE PARTITION PROBLEMS." Bulletin of informatics and cybernetics 31, no. 1 (March 1999): 67–90. http://dx.doi.org/10.5109/13481.

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8

Chu, Moody T. "Inverse Eigenvalue Problems." SIAM Review 40, no. 1 (January 1998): 1–39. http://dx.doi.org/10.1137/s0036144596303984.

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9

Greensite, Fred. "Partial inverse problems." Inverse Problems 22, no. 2 (March 6, 2006): 461–79. http://dx.doi.org/10.1088/0266-5611/22/2/005.

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10

Isakov, Victor. "Inverse obstacle problems." Inverse Problems 25, no. 12 (November 23, 2009): 123002. http://dx.doi.org/10.1088/0266-5611/25/12/123002.

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11

Horváth, Miklós, and Orsolya Sáfár. "Inverse eigenvalue problems." Journal of Mathematical Physics 57, no. 11 (November 2016): 112102. http://dx.doi.org/10.1063/1.4964390.

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12

Klawonn, David. "Inverse nodal problems." Journal of Physics A: Mathematical and Theoretical 42, no. 17 (April 7, 2009): 175209. http://dx.doi.org/10.1088/1751-8113/42/17/175209.

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13

Carlisle Thacker, Williams. "Oceanographic inverse problems." Physica D: Nonlinear Phenomena 60, no. 1-4 (November 1992): 16–37. http://dx.doi.org/10.1016/0167-2789(92)90224-b.

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14

Burkard, Rainer E., Carmen Pleschiutschnig, and Jianzhong Zhang. "Inverse median problems." Discrete Optimization 1, no. 1 (June 2004): 23–39. http://dx.doi.org/10.1016/j.disopt.2004.03.003.

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15

Antoniadis, Anestis, and Jéremie Bigot. "Poisson inverse problems." Annals of Statistics 34, no. 5 (October 2006): 2132–58. http://dx.doi.org/10.1214/009053606000000687.

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16

Chen, Hubie. "Inverse NP Problems." computational complexity 17, no. 1 (April 2008): 94–118. http://dx.doi.org/10.1007/s00037-008-0240-6.

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17

Gol'dman, N. L. "Inverse Stefan problems." Journal of Engineering Physics and Thermophysics 65, no. 6 (December 1993): 1189–94. http://dx.doi.org/10.1007/bf00861940.

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18

Benning, Martin, and Martin Burger. "Modern regularization methods for inverse problems." Acta Numerica 27 (May 1, 2018): 1–111. http://dx.doi.org/10.1017/s0962492918000016.

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Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research.In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.

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19

Il'yasov, Yavdat Shavkatovich, and Nurmukhamet Fuatovich Valeev. "On inverse spectral problem and generalized Sturm nodal theorem for nonlinear boundary value problems." Ufimskii Matematicheskii Zhurnal 10, no. 4 (2018): 122–28. http://dx.doi.org/10.13108/2018-10-4-122.

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20

Chung, Julianne, and Matthias Chung. "Optimal Regularized Inverse Matrices for Inverse Problems." SIAM Journal on Matrix Analysis and Applications 38, no. 2 (January 2017): 458–77. http://dx.doi.org/10.1137/16m1066531.

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21

Kubo, Shiro. "Computational Approaches to Inverse Problems : Inverse Analyses." Journal of the Society of Mechanical Engineers 98, no. 920 (1995): 567–69. http://dx.doi.org/10.1299/jsmemag.98.920_567.

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22

Shieh, Chung-Tsun, and V. A. Yurko. "Inverse nodal and inverse spectral problems for discontinuous boundary value problems." Journal of Mathematical Analysis and Applications 347, no. 1 (November 2008): 266–72. http://dx.doi.org/10.1016/j.jmaa.2008.05.097.

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23

Schönlieb, Carola-Bibiane, Juan Carlos De los Reyes, and Eldad Haber. "Preface for Inverse Problems special issue on learning and inverse problems." Inverse Problems 33, no. 7 (June 21, 2017): 070301. http://dx.doi.org/10.1088/1361-6420/aa7429.

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24

Mozgovoy, A. V. "Methods of constructing basis in solving inverse problems." Functional materials 21, no. 4 (December 30, 2014): 457–62. http://dx.doi.org/10.15407/fm21.04.457.

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25

Keneskyzy, K., and S. B. Yeskermes. "Метод машинного обучения для обратных задач теплопроводности." INTERNATIONAL JOURNAL OF INFORMATION AND COMMUNICATION TECHNOLOGIES 2, no. 1(5) (March 26, 2021): 59–64. http://dx.doi.org/10.54309/ijict.2021.05.1.008.

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Investigated in this work is the potential of carrying out inverse problems with linear and non-linear behavior using machine learning methods and the neural network method. With the advent of ma-chine learning algorithms it is now possible to model inverse problems faster and more accurately. In order to demonstrate the use of machine learning and neural networks in solving inverse problems, we propose a fusion between computational mechanics and machine learning. The forward problems are solved first to create a database. This database is then used to train the machine learning and neural network algorithms. The trained algorithm is then used to determine the boundary conditions of a problem from assumed meas-urements. The proposed method is tested for the linear/non-linear heat conduction problems in which the boundary conditions are determined by providing three, four, and five temperature measurements. This re-search demonstrates that the proposed fusion of computational mechanics and machine learning is an effec-tive way of tackling complex inverse problems.

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26

Berkshire, Frank, and G. M. L. Gladwell. "Inverse Problems in Vibration." Mathematical Gazette 71, no. 458 (December 1987): 343. http://dx.doi.org/10.2307/3617104.

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27

Kamenkov, M. V. "Problems of Inverse Possession." Actual Problems of Russian Law 17, no. 7 (June 22, 2022): 80–90. http://dx.doi.org/10.17803/1994-1471.2022.140.7.080-090.

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28

Gao, Weidong, Alfred Geroldinger, and Wolfgang A. Schmid. "Inverse zero-sum problems." Acta Arithmetica 128, no. 3 (2007): 245–79. http://dx.doi.org/10.4064/aa128-3-5.

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29

Real, Rommel. "Solving Inverse Problems Interestingly." International Journal of Applied Sciences and Smart Technologies 02, no. 01 (June 8, 2020): 1–8. http://dx.doi.org/10.24071/ijasst.v2i1.1972.

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30

Greenleaf, Allan, Yaroslav Kurylev, Matti Lassas, and Gunther Uhlmann. "Invisibility and inverse problems." Bulletin of the American Mathematical Society 46, no. 1 (October 14, 2008): 55–97. http://dx.doi.org/10.1090/s0273-0979-08-01232-9.

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31

Bates, R. H. T. "Inverse Problems in Astronomy." Physics Bulletin 37, no. 4 (April 1986): 177. http://dx.doi.org/10.1088/0031-9112/37/4/035.

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32

Wood, K., and G. K. Fox. "Inverse problems in spectropolarimetry." Inverse Problems 11, no. 4 (August 1, 1995): 795–821. http://dx.doi.org/10.1088/0266-5611/11/4/012.

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33

Evans, Steven N., and Philip B. Stark. "Inverse problems as statistics." Inverse Problems 18, no. 4 (May 21, 2002): R55—R97. http://dx.doi.org/10.1088/0266-5611/18/4/201.

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34

Bonnet, Marc, and Andrei Constantinescu. "Inverse problems in elasticity." Inverse Problems 21, no. 2 (February 24, 2005): R1—R50. http://dx.doi.org/10.1088/0266-5611/21/2/r01.

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35

Cavalier, L. "Nonparametric statistical inverse problems." Inverse Problems 24, no. 3 (May 23, 2008): 034004. http://dx.doi.org/10.1088/0266-5611/24/3/034004.

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36

Goodwin, Graham C. "INVERSE PROBLEMS WITH CONSTRAINTS." IFAC Proceedings Volumes 35, no. 1 (2002): 35–48. http://dx.doi.org/10.3182/20020721-6-es-1901.01638.

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37

Orlande, Helcio R. B. "Inverse Heat Transfer Problems." Heat Transfer Engineering 32, no. 9 (August 2011): 715–17. http://dx.doi.org/10.1080/01457632.2011.525128.

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38

Gladwell, Graham M. L. "Inverse Problems in Vibration." Applied Mechanics Reviews 39, no. 7 (July 1, 1986): 1013–18. http://dx.doi.org/10.1115/1.3149517.

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This article concerns infinitesimal free vibrations of undamped elastic systems of finite extent. A review is made of the literature relating to the unique reconstruction of a vibrating system from natural frequency data. The literature is divided into two groups—those papers concerning discrete systems, for which the inverse problems are closely related to matrix inverse eigenvalue problems, and those concerning continuous systems governed either by one or the other of the Sturm–Liouville equations or by the Euler–Bernoulli equation for flexural vibrations of a thin beam.

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39

Chu, Moody T., and Gene H. Golub. "Structured inverse eigenvalue problems." Acta Numerica 11 (January 2002): 1–71. http://dx.doi.org/10.1017/s0962492902000016.

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An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behaviour. Spectral information is entailed because the dynamical behaviour is often governed by the underlying natural frequencies and normal modes. Structural stipulation is designated because the physical system is often subject to some feasibility constraints. The spectral data involved may consist of complete or only partial information on eigenvalues or eigenvectors. The structure embodied by the matrices can take many forms. The objective of an inverse eigenvalue problem is to construct a matrix that maintains both the specific structure as well as the given spectral property. In this expository paper the emphasis is to provide an overview of the vast scope of this intriguing problem, treating some of its many applications, its mathematical properties, and a variety of numerical techniques.

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40

Cherepaschuk, A. M., A. V. Goncharski, and A. G. Yagola. "Inverse Problems in Astrophysics." International Astronomical Union Colloquium 90 (1986): 135–36. http://dx.doi.org/10.1017/s0252921100091351.

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41

Dmitriev, V. I. "Solving evolutionary inverse problems." Computational Mathematics and Modeling 22, no. 3 (July 2011): 342–46. http://dx.doi.org/10.1007/s10598-011-9105-y.

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42

Amirov, A. Kh. "Solvability of inverse problems." Siberian Mathematical Journal 28, no. 6 (1988): 865–72. http://dx.doi.org/10.1007/bf00969463.

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43

Dovì, V. G., H. Preisig, and O. Paladino. "Inverse free boundary problems." Applied Mathematics Letters 2, no. 1 (1989): 91–96. http://dx.doi.org/10.1016/0893-9659(89)90125-0.

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44

Lu, James, Elias August, and Heinz Koeppl. "Inverse problems from biomedicine." Journal of Mathematical Biology 67, no. 1 (April 18, 2012): 143–68. http://dx.doi.org/10.1007/s00285-012-0523-z.

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45

Anatychuk, L. I., O. J. Luste, R. V. Kuz, and M. N. Strutinsky. "Inverse Problems of Thermoelectricity." Journal of Electronic Materials 40, no. 5 (March 11, 2011): 856–61. http://dx.doi.org/10.1007/s11664-011-1595-z.

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46

Yang, Chao, and Jianzhong Zhang. "Inverse maximum capacity problems." OR Spectrum 20, no. 2 (April 1, 1998): 97–100. http://dx.doi.org/10.1007/s002910050057.

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47

Ikramov, Kh D., and V. N. Chugunov. "Inverse matrix eigenvalue problems." Journal of Mathematical Sciences 98, no. 1 (January 2000): 51–136. http://dx.doi.org/10.1007/bf02355380.

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48

Solopchenko, G. N. "Inverse problems in measurement." Measurement 5, no. 1 (January 1987): 10–19. http://dx.doi.org/10.1016/0263-2241(87)90023-6.

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49

Vairaktaris, Emmanouil. "Inverse problems in geomechanics." European Journal of Environmental and Civil Engineering 14, no. 8-9 (September 2010): 1155–66. http://dx.doi.org/10.1080/19648189.2010.9693285.

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50

P., B., and G. M. L. Gladwell. "Inverse Problems in Vibration." Mathematics of Computation 52, no. 186 (April 1989): 717. http://dx.doi.org/10.2307/2008490.

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