Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products
On the basis of the Euler identity, we obtain expansions for weighted pseudoinverse matrices with positive-definite weights in infinite matrix power products of two types: with positive and negative exponents. We obtain estimates for the closeness of weighted pseudoinverse matrices and matrices obta...
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| Date: | 2004 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3864 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509999022735360 |
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| author | Galba, E. F. Deineka, V. S. Sergienko, I. V. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. |
| author_facet | Galba, E. F. Deineka, V. S. Sergienko, I. V. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. |
| author_sort | Galba, E. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:12:48Z |
| description | On the basis of the Euler identity, we obtain expansions for weighted pseudoinverse matrices with positive-definite weights in infinite matrix power products of two types: with positive and negative exponents. We obtain estimates for the closeness of weighted pseudoinverse matrices and matrices obtained on the basis of a fixed number of factors of matrix power products and terms of matrix power series. We compare the rates of convergence of expansions of weighted pseudoinverse matrices in matrix power series and matrix power products to weighted pseudoinverse matrices. We consider problems of construction and comparison of iterative processes of computation of weighted pseudoinverse matrices on the basis of the obtained expansions of these matrices. |
| first_indexed | 2026-03-24T02:50:01Z |
| format | Article |
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| id | umjimathkievua-article-3864 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:50:01Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d4/a4bce457b85649b2f577f87f5d79c9d4.pdf |
| spelling | umjimathkievua-article-38642020-03-18T20:12:48Z Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products Разложение взвешенных псевдообратных матриц в матричные степенные произведения Galba, E. F. Deineka, V. S. Sergienko, I. V. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. On the basis of the Euler identity, we obtain expansions for weighted pseudoinverse matrices with positive-definite weights in infinite matrix power products of two types: with positive and negative exponents. We obtain estimates for the closeness of weighted pseudoinverse matrices and matrices obtained on the basis of a fixed number of factors of matrix power products and terms of matrix power series. We compare the rates of convergence of expansions of weighted pseudoinverse matrices in matrix power series and matrix power products to weighted pseudoinverse matrices. We consider problems of construction and comparison of iterative processes of computation of weighted pseudoinverse matrices on the basis of the obtained expansions of these matrices. На основі тотожності Ей л ера одержано розвинення зважених псевдообернених матриць з додатно означеними вагами у нескінченні матричні степеневі добутки двох типів: з додатними і від'ємними показниками степенів. Встановлено оцінки близькості зважених псевдообернених матриць та матриць, отриманих на основі фіксованого числа співмножників матричних степеневих добутків та членів матричних степеневих рядів. Наведено порівняння швидкостей збіжності до зважених псевдообернених матриць їх розвинень в матричні степеневі ряди і в матричні степеневі добутки. Розглянуто питання побудови та порівняння ітераційиих процесів обчислення зважених псевдооберпепих матриць па основі одержаних розвинень цих матриць. Institute of Mathematics, NAS of Ukraine 2004-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3864 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 11 (2004); 1539-1556 Український математичний журнал; Том 56 № 11 (2004); 1539-1556 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3864/4447 https://umj.imath.kiev.ua/index.php/umj/article/view/3864/4448 Copyright (c) 2004 Galba E. F.; Deineka V. S.; Sergienko I. V. |
| spellingShingle | Galba, E. F. Deineka, V. S. Sergienko, I. V. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. Галба, Е. Ф. Дейнека, В. С. Сергиенко, И. В. Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products |
| title | Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products |
| title_alt | Разложение взвешенных псевдообратных
матриц в матричные степенные произведения |
| title_full | Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products |
| title_fullStr | Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products |
| title_full_unstemmed | Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products |
| title_short | Expansion of Weighted Pseudoinverse Matrices in Matrix Power Products |
| title_sort | expansion of weighted pseudoinverse matrices in matrix power products |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3864 |
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