Pub Date : 2018-07-11DOI: 10.1142/9789813238671_0005
{"title":"Symbolic computation of generalized inverses","authors":"","doi":"10.1142/9789813238671_0005","DOIUrl":"https://doi.org/10.1142/9789813238671_0005","url":null,"abstract":"","PeriodicalId":252855,"journal":{"name":"Numerical and Symbolic Computations of Generalized Inverses","volume":"102 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123167071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-11DOI: 10.1142/9789813238671_0002
{"title":"Basic notions from matrix theory, optimization and theory of generalized inverses","authors":"","doi":"10.1142/9789813238671_0002","DOIUrl":"https://doi.org/10.1142/9789813238671_0002","url":null,"abstract":"","PeriodicalId":252855,"journal":{"name":"Numerical and Symbolic Computations of Generalized Inverses","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114281504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-11DOI: 10.1142/9789813238671_0006
W. Rising
First it is shown that any generalized inverse of the infinitesimal generator of an irreducible Markov chain can be used to compute the exact stationary distribution and all the expected first-passage times of the chain. In the special case of a single-server queue this allows all computations to be done with upper-triangular matrices. Next it is shown that the effect of a perturbation of the infinitesimal generator on the stationary distribution and expected first-passage times can also be computed using generalized inverses. These results extend and generalize Schweitzer's [9] original work using fundamental matrices. It is then shown that any perturbation can be broken up into a series of perturbations each involving a single state. BISTABLE QUEUES; FIRST-PASSAGE TIMES
{"title":"Applications of generalized inverses","authors":"W. Rising","doi":"10.1142/9789813238671_0006","DOIUrl":"https://doi.org/10.1142/9789813238671_0006","url":null,"abstract":"First it is shown that any generalized inverse of the infinitesimal generator of an irreducible Markov chain can be used to compute the exact stationary distribution and all the expected first-passage times of the chain. In the special case of a single-server queue this allows all computations to be done with upper-triangular matrices. Next it is shown that the effect of a perturbation of the infinitesimal generator on the stationary distribution and expected first-passage times can also be computed using generalized inverses. These results extend and generalize Schweitzer's [9] original work using fundamental matrices. It is then shown that any perturbation can be broken up into a series of perturbations each involving a single state. BISTABLE QUEUES; FIRST-PASSAGE TIMES","PeriodicalId":252855,"journal":{"name":"Numerical and Symbolic Computations of Generalized Inverses","volume":"301 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122797072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-11DOI: 10.1142/9789813238671_fmatter
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789813238671_fmatter","DOIUrl":"https://doi.org/10.1142/9789813238671_fmatter","url":null,"abstract":"","PeriodicalId":252855,"journal":{"name":"Numerical and Symbolic Computations of Generalized Inverses","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125856748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-07-11DOI: 10.1142/9789813238671_0003
{"title":"Direct methods for computing generalized inverses","authors":"","doi":"10.1142/9789813238671_0003","DOIUrl":"https://doi.org/10.1142/9789813238671_0003","url":null,"abstract":"","PeriodicalId":252855,"journal":{"name":"Numerical and Symbolic Computations of Generalized Inverses","volume":"424 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121825637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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