A discrete algorithm for localizing the discontinuity lines of a function of two variables
We consider an ill-posed problem of localizing the discontinuity lines of a function of two variables. It is assumed that, instead of a precisely given function f , the values are available of the averages on the square of the perturbed function f δ at the points of a uniform grid as well as the err...
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| Veröffentlicht in: | Journal of applied and industrial mathematics 2017-10, Vol.11 (4), p.463-471 |
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| creator | Ageev, A. L. Antonova, T. V. |
| description | We consider an ill-posed problem of localizing the discontinuity lines of a function of two variables. It is assumed that, instead of a precisely given function
f
, the values are available of the averages on the square of the perturbed function
f
δ
at the points of a uniform grid as well as the error level δ so that
‖
f
−
f
δ
‖
L
2
(
ℝ
2
)
≤ δ. An algorithm is constructed for localizing the discontinuity lines, its convergence is proved with the estimates of the approximation accuracy, which coincide in the order of magnitude with the estimates obtained earlier by the authors for the case when, instead of the average values of the function
f
δ
, the function itself is given. Also, we substantiate the estimates for an important characteristic of localization methods, i.e. separability threshold. |
| doi_str_mv | 10.1134/S1990478917040019 |
| format | Article |
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f
, the values are available of the averages on the square of the perturbed function
f
δ
at the points of a uniform grid as well as the error level δ so that
‖
f
−
f
δ
‖
L
2
(
ℝ
2
)
≤ δ. An algorithm is constructed for localizing the discontinuity lines, its convergence is proved with the estimates of the approximation accuracy, which coincide in the order of magnitude with the estimates obtained earlier by the authors for the case when, instead of the average values of the function
f
δ
, the function itself is given. Also, we substantiate the estimates for an important characteristic of localization methods, i.e. separability threshold.</description><identifier>ISSN: 1990-4789</identifier><identifier>EISSN: 1990-4797</identifier><identifier>DOI: 10.1134/S1990478917040019</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Discontinuity ; Estimates ; Ill posed problems ; Mathematical analysis ; Mathematics ; Mathematics and Statistics</subject><ispartof>Journal of applied and industrial mathematics, 2017-10, Vol.11 (4), p.463-471</ispartof><rights>Pleiades Publishing, Ltd. 2017</rights><rights>Copyright Springer Science & Business Media Oct 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2319-7ca24c5b8c9de5cdacaa8a048203933441510098b1ea5093105485fddfa123e53</citedby><cites>FETCH-LOGICAL-c2319-7ca24c5b8c9de5cdacaa8a048203933441510098b1ea5093105485fddfa123e53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1990478917040019$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1990478917040019$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Ageev, A. L.</creatorcontrib><creatorcontrib>Antonova, T. V.</creatorcontrib><title>A discrete algorithm for localizing the discontinuity lines of a function of two variables</title><title>Journal of applied and industrial mathematics</title><addtitle>J. Appl. Ind. Math</addtitle><description>We consider an ill-posed problem of localizing the discontinuity lines of a function of two variables. It is assumed that, instead of a precisely given function
f
, the values are available of the averages on the square of the perturbed function
f
δ
at the points of a uniform grid as well as the error level δ so that
‖
f
−
f
δ
‖
L
2
(
ℝ
2
)
≤ δ. An algorithm is constructed for localizing the discontinuity lines, its convergence is proved with the estimates of the approximation accuracy, which coincide in the order of magnitude with the estimates obtained earlier by the authors for the case when, instead of the average values of the function
f
δ
, the function itself is given. Also, we substantiate the estimates for an important characteristic of localization methods, i.e. separability threshold.</description><subject>Discontinuity</subject><subject>Estimates</subject><subject>Ill posed problems</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1990-4789</issn><issn>1990-4797</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kEtLAzEUhYMoWLQ_wF3A9WhuHjPJshRfUHChbtwMmUymjUyTmmSU-uudWhFBXN0H3zkHDkJnQC4AGL98AKUIr6SCinBCQB2gye5V8EpVhz-7VMdompJrCANasrKkE_Q8w61LJtpsse6XIbq8WuMuRNwHo3v34fwS55X9ooLPzg8ub3HvvE04dFjjbvAmu-B3V34P-E1Hp5veplN01Ok-2en3PEFP11eP89ticX9zN58tCkMZqKIymnIjGmlUa4VptdFaasIlJUwxxjkIIETJBqwWRDEggkvRtW2ngTIr2Ak63_tuYngdbMr1SxiiHyNrUKUklDElRwr2lIkhpWi7ehPdWsdtDaTetVj_aXHU0L0mjaxf2vjL-V_RJ1tvc4k</recordid><startdate>20171001</startdate><enddate>20171001</enddate><creator>Ageev, A. 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f
, the values are available of the averages on the square of the perturbed function
f
δ
at the points of a uniform grid as well as the error level δ so that
‖
f
−
f
δ
‖
L
2
(
ℝ
2
)
≤ δ. An algorithm is constructed for localizing the discontinuity lines, its convergence is proved with the estimates of the approximation accuracy, which coincide in the order of magnitude with the estimates obtained earlier by the authors for the case when, instead of the average values of the function
f
δ
, the function itself is given. Also, we substantiate the estimates for an important characteristic of localization methods, i.e. separability threshold.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1990478917040019</doi><tpages>9</tpages></addata></record> |
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| identifier | ISSN: 1990-4789 |
| ispartof | Journal of applied and industrial mathematics, 2017-10, Vol.11 (4), p.463-471 |
| issn | 1990-4789 1990-4797 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Discontinuity Estimates Ill posed problems Mathematical analysis Mathematics Mathematics and Statistics |
| title | A discrete algorithm for localizing the discontinuity lines of a function of two variables |
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