Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Alexander S. Leonov"'
Publikováno v:
Journal of Inverse and Ill-posed Problems. 30:23-34
A fast algorithm for calculating the gradient of the Tikhonov functional is proposed for solving inverse coefficient problems for linear partial differential equations of a general form by the regularization method. The algorithm is designed for prob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ab207b03c45c5dc76cc4d90bfacebd2f
https://doi.org/10.1515/jiip-2020-0109
https://doi.org/10.1515/jiip-2020-0109
Publikováno v:
Journal of Applied and Industrial Mathematics. 14:802-810
Under consideration is the problem of improving the contrast of the image obtained by processing tomographic projections with phase distortion. The study is based on the well-known intensity transfer equation. Unlike other works, this equation is sol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fac6f71509f4896a03d291bcc4da93e2
https://doi.org/10.1134/s1990478920040171
https://doi.org/10.1134/s1990478920040171
Autor:
Alexander S. Leonov
Publikováno v:
Journal of Inverse and Ill-posed Problems. 28:677-692
We consider inverse problems of recovering a source term in initial boundary value problems for linear multidimensional partial differential equations (PDEs) of a general form. A universal stable method suitable for solving such inverse problems is p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::261a12e77ee9479b5d65c1711aedb5b3
https://doi.org/10.1515/jiip-2020-0055
https://doi.org/10.1515/jiip-2020-0055
Publikováno v:
Inverse Problems in Science and Engineering. 29:1055-1069
We study the three-dimensional inverse problem of elastography, that is finding the Young's modulus of a biological tissue from known values of its vertical displacements. In this way, one can find...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bc2bf0084ac6c030b9bf2e4d877f7bbc
https://doi.org/10.1080/17415977.2020.1817006
https://doi.org/10.1080/17415977.2020.1817006
Autor:
Alexander S. Leonov
Publikováno v:
Computational Mathematics and Mathematical Physics. 60:960-986
A new direction in methods for solving ill-posed problems, namely, the theory of regularizing algorithms with approximate solutions of extra-optimal quality is surveyed. A distinctive feature of these methods is that they are optimal not only in the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dd35738cf23dcaac055f73cb72b8edcc
https://doi.org/10.1134/s0965542520060068
https://doi.org/10.1134/s0965542520060068
Publikováno v:
Computational Mathematics and Mathematical Physics. 60:987-999
A new algorithm is proposed for solving a three-dimensional scalar inverse problem of acoustic sensing in an inhomogeneous medium with given complex wave field amplitudes measured outside the inhomogeneity region. In the case of data measured in a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0fbfc1dd68a9905ddf3b9fe51b30bcb9
https://doi.org/10.1134/s0965542520060032
https://doi.org/10.1134/s0965542520060032
Autor:
Alexander S. Leonov
Publikováno v:
Russian Mathematics. 64:26-34
We consider extremal problems introduced and investigated earlier by the author for calculating global and local a posteriori error estimates of approximate solutions to ill-posed inverse problems. For linear inverse problems in Hilbert spaces, they
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a3fc04de62a9ccb230297aea1fff196b
https://doi.org/10.3103/s1066369x20020048
https://doi.org/10.3103/s1066369x20020048
Publikováno v:
Numerical Analysis and Applications. 12:311-325
A three-dimensional coefficient inverse problem for the wave equation (with losses) in a cylindrical domain is considered. The data given for its solution are special time integrals of a wave field measured in a cylindrical layer. We present and subs
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dd16ff1e4036c22eb7ce5b6f8909b0e3
https://doi.org/10.1134/s1995423919040013
https://doi.org/10.1134/s1995423919040013
Publikováno v:
Moscow University Physics Bulletin. 74:488-493
The paper presents the solution of a special three-dimensional inverse elastography problem: given a quasistatic model of a linear-elastic isotropic body subject to surface forces, to find the Young’s modulus distribution in the biological tissues
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1571f18873ec37626f6ad50e33a04545
https://doi.org/10.3103/s0027134919050096
https://doi.org/10.3103/s0027134919050096
Autor:
Alexander S. Leonov
Publikováno v:
Mathematical Notes. 105:385-397
The notion of the quality of approximate solutions of ill-posed extremum problems is introduced and a posteriori estimates of quality are studied for various solution methods. Several examples of quality functionals which can be used to solve practic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cd13ce4e547882baf289984219d3f889
https://doi.org/10.1134/s000143461903009x
https://doi.org/10.1134/s000143461903009x