{"title":"Chapter 20: LU factorization","authors":"","doi":"10.1137/1.9781611975703.ch20","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch20","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115007887","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}
{"title":"Back Matter","authors":"","doi":"10.1137/1.9781611975703.bm","DOIUrl":"https://doi.org/10.1137/1.9781611975703.bm","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128381530","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}
{"title":"Chapter 13: Differentiation","authors":"","doi":"10.1137/1.9781611975703.ch13","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch13","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121423687","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}
{"title":"Chapter 33: Nonlinear differential equations on piecewise-uniform grids","authors":"","doi":"10.1137/1.9781611975703.ch33","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch33","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125581687","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}
{"title":"Chapter 25: Collocation on a piecewise-uniform grid","authors":"","doi":"10.1137/1.9781611975703.ch25","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch25","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129905780","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}
{"title":"Chapter 5: Floating-point arithmetic","authors":"","doi":"10.1137/1.9781611975703.ch5","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch5","url":null,"abstract":"Fixed point numbers suffer from limited range and accuracy. For a given word length both fixed point and floating point representations give equal distinct numbers. The difference is that in fixed point representation the spacing between the numbers is equal, so smaller numbers when truncated or rounded give a much larger error than the larger numbers. However floating point representation gives different spacing between numbers. We get denser distances between numbers when the number is small and sparser distance for larger numbers. So the absolute representation error increases with larger numbers.","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127351917","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}
{"title":"Chapter 30: Zeros as eigenvalues","authors":"","doi":"10.1137/1.9781611975703.ch30","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch30","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122497109","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}
{"title":"Chapter 4: Experimental accuracy analysis for functions","authors":"","doi":"10.1137/1.9781611975703.ch4","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch4","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121748420","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}
{"title":"Chapter 14: Integration of a polynomial interpolant","authors":"","doi":"10.1137/1.9781611975703.ch14","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch14","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128117174","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}
{"title":"Chapter 11: Accuracy of Chebyshev interpolation","authors":"","doi":"10.1137/1.9781611975703.ch11","DOIUrl":"https://doi.org/10.1137/1.9781611975703.ch11","url":null,"abstract":"","PeriodicalId":394559,"journal":{"name":"Numerical Analysis: Theory and Experiments","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132018677","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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