Implicit restart scheme for large scale Krylov subspace model reduction method

Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century. Pub Date : 2001-12-28 DOI:10.1109/INMIC.2001.995327

N. Ahmed, M.M. Awais

{"title":"Implicit restart scheme for large scale Krylov subspace model reduction method","authors":"N. Ahmed, M.M. Awais","doi":"10.1109/INMIC.2001.995327","DOIUrl":null,"url":null,"abstract":"An implicitly restarted Krylov subspace model reduction method is presented. By this technique a stable, linear transfer function f(s) of order n can be approximated by an order m, where n/spl Gt/m. The oblique projection of stable systems onto a Krylov subspace may generate unstable partial realizations along with undesirable modes. To ensure that the Krylov projected model for a stable system is also stable and contains useful modes only, further operations like stable projection and balanced truncation are then performed to compute a reduced order model f/sub r/(s) of order r (where r<m), which approximates more accurately the original system. This all is imperative because the robust controller design methods based on the small gain theorem require that the actual model f(s)and the nominal model (f,(s)) have the same number of poles in the closed right half complex plane It can be realized that both these projections may be combined as a single oblique projection and this whole process can be fitted into an implicit restart framework. The behavior of the developed algorithm is illustrated by taking a large-scale system. Finally, a criterion for the selection of an accurate reduced order model approximation is proposed for large-scale systems.","PeriodicalId":286459,"journal":{"name":"Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/INMIC.2001.995327","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 4

Abstract

An implicitly restarted Krylov subspace model reduction method is presented. By this technique a stable, linear transfer function f(s) of order n can be approximated by an order m, where n/spl Gt/m. The oblique projection of stable systems onto a Krylov subspace may generate unstable partial realizations along with undesirable modes. To ensure that the Krylov projected model for a stable system is also stable and contains useful modes only, further operations like stable projection and balanced truncation are then performed to compute a reduced order model f/sub r/(s) of order r (where r

查看原文本刊更多论文

大规模Krylov子空间模型约简方法的隐式重启方案

提出了一种隐式重启Krylov子空间模型约简方法。通过这种技术，n阶的稳定的线性传递函数f(s)可以用m阶近似，其中n/spl Gt/m。稳定系统在Krylov子空间上的斜投影可能产生不稳定的部分实现以及不期望的模态。为了确保稳定系统的Krylov投影模型也是稳定的并且只包含有用的模式，然后执行稳定投影和平衡截断等进一步的操作来计算r阶(其中r

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century.

自引率

0.00%

发文量

京公网安备 11010802042870号

Book学术文献互助群
群号：481959085