Pub Date : 2005-07-01DOI: 10.1137/1.9780898718157.ch4
S. Hammarling
This report is concerned with the quality of the computed numerical solutions of mathematical problems. We give an introduction to ideas that are important in understanding and measuring the quality of computed solutions. In particular we review the ideas of condition, stability and error analysis, and their realisation in numerical software. A number of illustrative examples are given.
{"title":"4. An Introduction to the Quality of Computed Solutions","authors":"S. Hammarling","doi":"10.1137/1.9780898718157.ch4","DOIUrl":"https://doi.org/10.1137/1.9780898718157.ch4","url":null,"abstract":"This report is concerned with the quality of the computed numerical solutions of mathematical problems. We give an introduction to ideas that are important in understanding and measuring the quality of computed solutions. In particular we\u0000review the ideas of condition, stability and error analysis, and their realisation in numerical software. A number of illustrative examples are given.","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124189709","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 : 1900-01-01DOI: 10.1137/1.9780898718157.CH11
C. Douglas, H. Langtangen
{"title":"11. Hardware-Assisted Algorithms","authors":"C. Douglas, H. Langtangen","doi":"10.1137/1.9780898718157.CH11","DOIUrl":"https://doi.org/10.1137/1.9780898718157.CH11","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125103688","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 : 1900-01-01DOI: 10.1137/1.9780898718157.CH9
G. Walster
{"title":"9. The Use and Implementation of Interval Data Types","authors":"G. Walster","doi":"10.1137/1.9780898718157.CH9","DOIUrl":"https://doi.org/10.1137/1.9780898718157.CH9","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124208603","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 : 1900-01-01DOI: 10.1137/1.9780898718157.ch8
B. Einarsson, B. Wichmann, K. Dritz, C. Douglas, H. Langtangen, V. Snyder, R. Boisvert, R. Pozo
{"title":"8. General Methods for Implementing Reliable and Correct Software","authors":"B. Einarsson, B. Wichmann, K. Dritz, C. Douglas, H. Langtangen, V. Snyder, R. Boisvert, R. Pozo","doi":"10.1137/1.9780898718157.ch8","DOIUrl":"https://doi.org/10.1137/1.9780898718157.ch8","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126177337","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 : 1900-01-01DOI: 10.1137/1.9780898718157.CH1
B. Einarsson
{"title":"1. What Can Go Wrong in Scientific Computing?","authors":"B. Einarsson","doi":"10.1137/1.9780898718157.CH1","DOIUrl":"https://doi.org/10.1137/1.9780898718157.CH1","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125124667","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 : 1900-01-01DOI: 10.1137/1.9780898718157.ch6
F. Chaitin-Chatelin, Elisabeth Traviesas-Cassan
{"title":"6. PRECISE and the Quality of Reliable Numerical Software","authors":"F. Chaitin-Chatelin, Elisabeth Traviesas-Cassan","doi":"10.1137/1.9780898718157.ch6","DOIUrl":"https://doi.org/10.1137/1.9780898718157.ch6","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125225341","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 : 1900-01-01DOI: 10.1137/1.9780898718157.ch12
W. Gropp
Parallel computing, as used in technical computing, is fundamentally about achieving higher performance than is possible with a uniprocessor. The unique issues for accurate and reliable computing are thus directly related to this desire for performance. This chapter briefly covers the major types of parallel computers, the programming models used with them, and issues in the choice and implementation of algorithms.
{"title":"12. Issues in Accurate and Reliable Use of Parallel Computing in Numerical Programs","authors":"W. Gropp","doi":"10.1137/1.9780898718157.ch12","DOIUrl":"https://doi.org/10.1137/1.9780898718157.ch12","url":null,"abstract":"Parallel computing, as used in technical computing, is fundamentally about achieving higher performance than is possible with a uniprocessor. The unique issues for accurate and reliable computing are thus directly related to this desire for performance. This chapter briefly covers the major types of parallel computers, the programming models used with them, and issues in the choice and implementation of algorithms.","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128079544","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 : 1900-01-01DOI: 10.1137/1.9780898718157.ch2
R. Boisvert, R. Cools, B. Einarsson
{"title":"2. Assessment of Accuracy and Reliability","authors":"R. Boisvert, R. Cools, B. Einarsson","doi":"10.1137/1.9780898718157.ch2","DOIUrl":"https://doi.org/10.1137/1.9780898718157.ch2","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127902391","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 : 1900-01-01DOI: 10.1137/1.9780898718157.CH10
S. Rump
10.
10.
{"title":"10. Computer-Assisted Proofs and Self-Validating Methods","authors":"S. Rump","doi":"10.1137/1.9780898718157.CH10","DOIUrl":"https://doi.org/10.1137/1.9780898718157.CH10","url":null,"abstract":"10.","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128152138","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 : 1900-01-01DOI: 10.1137/1.9780898718157.ch3
R. Cools
{"title":"3. Approximating Integrals, Estimating Errors, and Giving the Wrong Solution for a Deceptively Easy Problem","authors":"R. Cools","doi":"10.1137/1.9780898718157.ch3","DOIUrl":"https://doi.org/10.1137/1.9780898718157.ch3","url":null,"abstract":"","PeriodicalId":422759,"journal":{"name":"Accuracy and Reliability in Scientific Computing","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125621898","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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