Estimates for the Quantized Tensor Train Ranks for the Power Functions
In this work, we provide theoretical estimates for the ranks of the power functions , in the quantized tensor train (QTT) format for . Such functions and their several generalizations (e.g., ) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equa...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2024-07, Vol.45 (7), p.3182-3187 |
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| container_title | Lobachevskii journal of mathematics |
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| creator | Smirnov, M. S. Matveev, S. A. |
| description | In this work, we provide theoretical estimates for the ranks of the power functions
,
in the quantized tensor train (QTT) format for
. Such functions and their several generalizations (e.g.,
) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equations. In order to support the constructed theory we verify the values of QTT-ranks of these functions in practice with the use of the TTSVD procedure and show an agreement between the numerical and analytical results. |
| doi_str_mv | 10.1134/S1995080224603734 |
| format | Article |
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,
in the quantized tensor train (QTT) format for
. Such functions and their several generalizations (e.g.,
) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equations. In order to support the constructed theory we verify the values of QTT-ranks of these functions in practice with the use of the TTSVD procedure and show an agreement between the numerical and analytical results.</description><identifier>ISSN: 1995-0802</identifier><identifier>EISSN: 1818-9962</identifier><identifier>DOI: 10.1134/S1995080224603734</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Algebra ; Analysis ; Asymptotic methods ; Estimates ; Geometry ; Kinetic equations ; Mathematical Logic and Foundations ; Mathematics ; Mathematics and Statistics ; Probability Theory and Stochastic Processes ; Tensors</subject><ispartof>Lobachevskii journal of mathematics, 2024-07, Vol.45 (7), p.3182-3187</ispartof><rights>Pleiades Publishing, Ltd. 2024</rights><rights>Pleiades Publishing, Ltd. 2024.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c241t-ad14618e11065795ff2e5827590c7d620e05d6d41571658434c499b824d70a973</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/S1995080224603734$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1995080224603734$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Smirnov, M. S.</creatorcontrib><creatorcontrib>Matveev, S. A.</creatorcontrib><title>Estimates for the Quantized Tensor Train Ranks for the Power Functions</title><title>Lobachevskii journal of mathematics</title><addtitle>Lobachevskii J Math</addtitle><description>In this work, we provide theoretical estimates for the ranks of the power functions
,
in the quantized tensor train (QTT) format for
. Such functions and their several generalizations (e.g.,
) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equations. In order to support the constructed theory we verify the values of QTT-ranks of these functions in practice with the use of the TTSVD procedure and show an agreement between the numerical and analytical results.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Asymptotic methods</subject><subject>Estimates</subject><subject>Geometry</subject><subject>Kinetic equations</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Tensors</subject><issn>1995-0802</issn><issn>1818-9962</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNuC59VMvnOU0lqh4Nd6DnE3q1s1W5Msor_elBV6EE8zzPu8M8yL0CngcwDKLh5Aa44VJoQJTCVle2gCClSptSD7uc9yudUP0VGMa5xBIcQELeYxde82uVi0fSjSiyvuButT9-2aonI-5mEVbOeLe-tfd9Bt_-lCsRh8nbrex2N00Nq36E5-6xQ9LubVbFmubq6uZ5ersiYMUmkbYAKUA8CCS83bljiuiOQa17IRBDvMG9Ew4BIEV4yymmn9pAhrJLZa0ik6G_duQv8xuJjMuh-CzycNBVBES41FpmCk6tDHGFxrNiE_Gb4MYLONy_yJK3vI6ImZ9c8u7Db_b_oBJCJpgQ</recordid><startdate>20240701</startdate><enddate>20240701</enddate><creator>Smirnov, M. S.</creator><creator>Matveev, S. A.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240701</creationdate><title>Estimates for the Quantized Tensor Train Ranks for the Power Functions</title><author>Smirnov, M. S. ; Matveev, S. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c241t-ad14618e11065795ff2e5827590c7d620e05d6d41571658434c499b824d70a973</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Asymptotic methods</topic><topic>Estimates</topic><topic>Geometry</topic><topic>Kinetic equations</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Smirnov, M. S.</creatorcontrib><creatorcontrib>Matveev, S. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Lobachevskii journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Smirnov, M. S.</au><au>Matveev, S. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimates for the Quantized Tensor Train Ranks for the Power Functions</atitle><jtitle>Lobachevskii journal of mathematics</jtitle><stitle>Lobachevskii J Math</stitle><date>2024-07-01</date><risdate>2024</risdate><volume>45</volume><issue>7</issue><spage>3182</spage><epage>3187</epage><pages>3182-3187</pages><issn>1995-0802</issn><eissn>1818-9962</eissn><abstract>In this work, we provide theoretical estimates for the ranks of the power functions
,
in the quantized tensor train (QTT) format for
. Such functions and their several generalizations (e.g.,
) play an important role in studies of the asymptotic solutions of the aggregation-fragmentation kinetic equations. In order to support the constructed theory we verify the values of QTT-ranks of these functions in practice with the use of the TTSVD procedure and show an agreement between the numerical and analytical results.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1995080224603734</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Algebra Analysis Asymptotic methods Estimates Geometry Kinetic equations Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Tensors |
| title | Estimates for the Quantized Tensor Train Ranks for the Power Functions |
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