Article

The reconstruction and decomposition matrixes for linear splines

DOI:10.15622/sp.18.9
Authors:
Anton Alexandrovich Makarov
Anton Alexandrovich Makarov
Anton Alexandrovich Makarov
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Download citation
To read the full-text of this research, you can request a copy directly from the author.

Abstract

The aim of the paper is construction of calibration relations in the case of class of coordinate non-polynomial splines connected with refinement of grids. An embed\-ding of spline spaces is established for arbitrary refinement of grids. The reconstruction matrixes in the case of a grid on an open interval and a grid on a segment are constructed. The system of biorthogonal linear functionals to splines is constructed. The decomposition matrixes in the case of a grid on an open interval and a grid on a segment are constructed.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the author.

ResearchGate has not been able to resolve any citations for this publication.
Âýéâëåòû â îáðàáîòêå ñèãíàëîâ: Ïåð. ñ àíãë
  • Jan 2005
  • Ñ Ìàëëà
Ìàëëà Ñ. Âýéâëåòû â îáðàáîòêå ñèãíàëîâ: Ïåð. ñ àíãë. ß. Ì. AEèëåéêèíà. Ì.: Ìèð, 2005. 671 ñ.
Research area: computational mathematics, approximation, interpolation, splines, wavelets, digital signal processing, data compression, parallel algorithms, computer aided geometric design. Number of publications 35
  • Anton A Makarov
Anton A. Makarov PhD in Computer Science, Teaching assistant of Parallel Algorithms Department, St.-Petersburg State University. Research area: computational mathematics, approximation, interpolation, splines, wavelets, digital signal processing, data compression, parallel algorithms, computer aided geometric design. Number of publications 35. Antony.Makarov@gmail.com; St.-Petersburg State University, Universitetsky pr., 28, Petrodvorets, St. Petersburg, 198504, Russia. Ïîääåðaeêà èññëåäîâàíèé. Ðàáîòà âûïîëíåíà ïðè ÷àñòè÷íîé ôèíàíñîâîé ïîääåðaeêå ÊÍÂØ Ïðàâèòåëüñòâà Ñàíêò-Ïåòåðáóðãà.
Ìàòðèöû ðåêîíñòðóêöèè è êàëèáðîâî÷íûå ñîîòíîøåíèÿ äëÿ ìèíèìàëüíûõ ñïëàéíîâ // Ïðîáëåìû ìàòåì. àíàëèçà. Âûï. 60. Ìåaeâóç. ñá. / Ïîä ðåä. Í. Í. Óðàëüöåâîé. Íîâîñèáèðñê: Èçä-âî Ò. Ðîaeêîâñêàÿ, 2011. Ñ. 3952. English transl
  • Jan 2011
  • J Math Sci
  • 605621
  • À À Ìàêàðîâ
Ìàêàðîâ À. À. Ìàòðèöû ðåêîíñòðóêöèè è êàëèáðîâî÷íûå ñîîòíîøåíèÿ äëÿ ìèíèìàëüíûõ ñïëàéíîâ // Ïðîáëåìû ìàòåì. àíàëèçà. Âûï. 60. Ìåaeâóç. ñá. / Ïîä ðåä. Í. Í. Óðàëüöåâîé. Íîâîñèáèðñê: Èçä-âî Ò. Ðîaeêîâñêàÿ, 2011. Ñ. 3952. English transl.: J. Math. Sci., New York 178 (2011), no. 6, 605621.
ISSN 2078-9181 (печ.), ISSN 2078-9599 (онлайн) SPIIRAS Proceedings
  • Jan 2011
  • Спииран Труды
Труды СПИИРАН. 2011. Вып. 3(18). ISSN 2078-9181 (печ.), ISSN 2078-9599 (онлайн) SPIIRAS Proceedings. 2011. Issue 3(18). ISSN 2078-9181 (print), ISSN 2078-9599 (online) www.proceedings.spiiras.nw.ru
  • Jan 2009
  • 156-631
  • À À Ìàêàðîâ
  • Âýéâëåòíîì Ðàçëîaeåíèè Ïðîñòðàíñòâ Ñïëàéíîâ Ïåðâîãî Ïîðÿäêà
Ìàêàðîâ À. À. Î âýéâëåòíîì ðàçëîaeåíèè ïðîñòðàíñòâ ñïëàéíîâ ïåðâîãî ïîðÿäêà // Ïðîáëåìû ìàòåì. àíàëèçà. Âûï. 38. Ìåaeâóç. ñá. / Ïîä ðåä. Í. Í. Óðàëüöåâîé. Íîâîñèáèðñê: Ò. Ðîaeêîâñêàÿ, 2008. Ñ. 4760. English transl.: J. Math. Sci., New York 156 (2009), no. 4, 617 631.
  • Jan 2011
  • 589604
  • English Transl
English transl.: J. Math. Sci., New York 178 (2011), no. 6, 589604.
Êóñî÷íî-íåïðåðûâíûå ñïëàéí-âýéâëåòû íà íåðàâíîìåðíîé ñåòêå // Òðóäû
  • À À Ìàêàðîâ
Ìàêàðîâ À. À. Êóñî÷íî-íåïðåðûâíûå ñïëàéí-âýéâëåòû íà íåðàâíîìåðíîé ñåòêå // Òðóäû ÑÏÈÈÐÀÍ. 2010. Âûï. 14. Ñ. 103131.
Ìàòåìàòè÷åñêèé àíàëèç íà ìíîãîîáðàçèÿõ. Ëàíü, ÑÏá
  • Jan 2005
  • Ì Ñïèâàê
Ñïèâàê Ì. Ìàòåìàòè÷åñêèé àíàëèç íà ìíîãîîáðàçèÿõ. Ëàíü, ÑÏá., 2005. 160 ñ.
Î âýéâëåòíîì ðàçëîaeåíèè ïðîñòðàíñòâ ñïëàéíîâ ïåðâîãî ïîðÿäêà // Ïðîáëåìû ìàòåì. àíàëèçà. Âûï. 38. Ìåaeâóç. ñá. / Ïîä ðåä
  • Jan 2008
  • 631
  • À À Ìàêàðîâ
Ìàêàðîâ À. À. Î âýéâëåòíîì ðàçëîaeåíèè ïðîñòðàíñòâ ñïëàéíîâ ïåðâîãî ïîðÿäêà // Ïðîáëåìû ìàòåì. àíàëèçà. Âûï. 38. Ìåaeâóç. ñá. / Ïîä ðåä. Í. Í. Óðàëüöåâîé. Íîâîñèáèðñê: Ò. Ðîaeêîâñêàÿ, 2008. Ñ. 4760. English transl.: J. Math. Sci., New York 156 (2009), no. 4, 617 631.