Ошибка
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering
  • Ошибка при загрузке модулей:Can't create/write to file '/var/lib/mysql/tmp/#sql_bd4_0.MYI' (Errcode: 30) SQL=SELECT id, title, module, position, content, showtitle, control, params FROM jos_modules AS m LEFT JOIN jos_modules_menu AS mm ON mm.moduleid = m.id WHERE m.published = 1 AND m.access <= 0 AND m.client_id = 0 AND ( mm.menuid = 8 OR mm.menuid = 0 ) ORDER BY position, ordering

DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Coefficients calculation of the best linear method for recovery of bounded analytic functions in a circle

Вестник МГСУ 4/2014
  • Ovchintsev Mikhail Petrovich - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Gusakova Ekaterina Mikhaylovna - Moscow State University of Civil Engineering (MGSU) Engineer of the second category, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 44-51

This paper considers the problem of optimal recovery of bounded analytic functions. Namely, the values of these functions are determined at the point from their values at n given points lying in the unit circle. At first, we recall the necessary basic concepts: error of approximation by some method (which is a complex function of n complex variables), the best approximation method. Some theorems from the works of K.U. Osipenko are discussed: on the existence of a best linear approximation method and on calculating the error of best recovery method. After that we write out the formula for finding the error of best approximation method of bounded analytic functions in a unit circle. The lemma of conformal invariance of optimal recovery problem of these functions follows. We prove that under conformal mapping of the unit circle onto itself the error of the best approximation method before mapping coincides with the error of the best approximation method after mapping. It is also proved that a linear best method after conformal mapping coincides with the linear best restore method before this mapping (wherein the problem of optimal recovery after mapping is considered on the images of n given points lying in the original unit circle). Finally, we consider the problem of optimal recovery of bounded analytic functions in a circle in special case when the given points coincide with the vertices of a regular n-gon, and the point itself coincides with its center (which coincides with the origin). We prove that all the coefficients of the best linear method in this case are identical (wherein we apply the lemma of conformal invariance of optimal recovery problem of bounded analytic functions). The formulas for calculating these coefficients are given (for this purpose we write out an integral). The result is the smart, simple formulas for calculating the coefficients of the best linear approximation method for this particular case.

DOI: 10.22227/1997-0935.2014.4.44-51

Библиографический список
  1. Osipenko K.Yu. Nailuchshee priblizhenie analiticheskikh funktsiy po informatsii ob ikh znacheniyakh v konechnom chisle tochek [The Best Approximation of Analytical Functions According to the Information on their Values in Finite Number of Points]. Matematicheskie zametki [Mathematical Notes]. 1976, vol. 19, no. 1, pp. 29—40.
  2. Osipenko K.Yu. Optimal'naya interpolyatsiya analiticheskikh funktsiy [Optimal Interpolation of Analytical Functions]. Matematicheskie zametki [Mathematical Notes]. 1972, vol.12, no. 4, pp. 465—476.
  3. Osipenko K.Yu. Nailuchshie metody priblizheniya analiticheskikh funktsiy, zadannykh s pogreshnost'yu [The Best Approximation Methods for Analytical Functions Given with a Precision]. Matematicheskiy sbornik [Mathematical Collection]. 1982, vol. 118 (160), pp. 350—370.
  4. Osipenko K.Yu. Zadacha Kheynsa i optimal'naya ekstrapolyatsiya analiticheskikh funktsiy, zadannykh s oshibkoy [Heinz Problem and Optimal Extrapolation for Analytical Functions, Given with an Error]. Matematicheskiy sbornik [Mathematical Collection]. 1985, vol. 126 (168), no.4, pp. 566—575.
  5. Osipenko K.Yu. O nailuchshikh i optimal'nykh kvadraturnykh formulakh na klassakh ogranichennykh analiticheskikh funktsiy [On the Best and Optimal Quadrature Formulas on the Classes of Finite Analytical Functions]. Izvestiya ANSSSR, ser. Matematika [News of the Academy of Sciences of the USSR. Mathematics Series]. 1988, vol. 52, no. 1, pp. 79—99.
  6. Bakhvalov N.S. Ob optimal'nosti lineynykh metodov priblizheniya operatorov na vypuklykh klassakh funktsiy [On the Optimality of the Linear Approximation Methods on the Classes of Convex Functions]. Vychislitel'naya matematika i matematicheskaya fizika [Numerical Mathematics and Mathematical Physics]. 1971, no. 4 (11), pp. 1014—1018.
  7. Tikhomirov V.M., Ioffe A.D. Teoriya ekstremal'nykh zadach [Theory of Extremum Problems]. Moscow, Nauka Publ., 1974, 479 p.
  8. Tikhomirov V.M., Alekseev V.N., Fomin S.V. Optimal'noe upravlenie [Optimal Management]. Moscow, Nauka Publ., 1979, 429 p.
  9. Micchelli C., Rivlin T. A Survey of Optimal Recovery, Optimal Estimation in Approximation Theory. N.Y., Plenum press., 1977, pp. 1—54.
  10. Micchelli C., Rivlin T. Lectures on Optimal Recovery. Lect. Notes. 1982, vol. 9, pp. 21—93.
  11. Bojanob B.D. Best Quadrature Formula for a Certain Class of Analytic Functions. Zastos, Mat, VXIV. 1974, pp. 441—447.
  12. Fisher S., Micchelli C. The N-width of Analytic Functions. Duke Math J. 1980, vol. 47, pp. 789—801.
  13. Rogosinski W., Shapiro H. On Certain Extremum Problems for Analytic Functions. Acta Math. 1953, vol. 90, pp. 287—318. DOI: 10.1007/BF02392438.
  14. Singer Y. Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces. Berlin, Springer – Verlag, 1970, 462 p.
  15. Osipenko K.Yu. O proizvedeniyakh Blyashke, naimenee uklonyayushchikhsya ot nulya [On the Blaschke Products, Minimally Deviating from Zero]. Matematicheskie zametki [Mathematical Notes]. 1990, vol. 47, no. 5, pp. 71—80.

Cкачать на языке оригинала

Результаты 1 - 1 из 1