{"title":"AAA rational approximation for time domain model order reduction","authors":"Giovanni Conni , Frank Naets , Karl Meerbergen","doi":"10.1016/j.aml.2024.109188","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper an extension of the Adaptive Antoulas-Anderson (AAA) Model Order Reduction (MOR) method to time-domain data is defined, referred to as Time-Domain AAA (TDAAA). Inspired by other rational approximation time-domain MOR methods, like Time-Domain Vector Fitting (TDVF) and Time-Domain Loewner Framework (TDLF), TDAAA combines the adaptivity and flexibility of the AAA method in the frequency domain with an error minimization in the time domain. This combination makes the method an interesting alternative to fully time-domain or frequency-domain MOR methods. A combination of AAA and TDVF is also proposed, called AAA-TDVF, where the initial TDVF poles are selected by AAA. This new poles initialization improves both accuracy and convergence speed. Both TDAAA and TDVF are discussed in detail and their performance is compared on a benchmark LTI system.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002088","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper an extension of the Adaptive Antoulas-Anderson (AAA) Model Order Reduction (MOR) method to time-domain data is defined, referred to as Time-Domain AAA (TDAAA). Inspired by other rational approximation time-domain MOR methods, like Time-Domain Vector Fitting (TDVF) and Time-Domain Loewner Framework (TDLF), TDAAA combines the adaptivity and flexibility of the AAA method in the frequency domain with an error minimization in the time domain. This combination makes the method an interesting alternative to fully time-domain or frequency-domain MOR methods. A combination of AAA and TDVF is also proposed, called AAA-TDVF, where the initial TDVF poles are selected by AAA. This new poles initialization improves both accuracy and convergence speed. Both TDAAA and TDVF are discussed in detail and their performance is compared on a benchmark LTI system.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.