{"title":"Value At Risk: Recent Advances","authors":"Irina Khindanova, S. Rachev","doi":"10.1201/9780429123610-18","DOIUrl":"https://doi.org/10.1201/9780429123610-18","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122314925","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":"Boundary Quadrature Formulas and Their Applications","authors":"He Tian-Xiao","doi":"10.1201/9780429123610-17","DOIUrl":"https://doi.org/10.1201/9780429123610-17","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123532393","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":"Trapezoidal-Type Rules from an Inequalities Point of View","authors":"P. Cerone, S. Dragomir","doi":"10.1201/9780429123610-3","DOIUrl":"https://doi.org/10.1201/9780429123610-3","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123341105","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":"Limit Theorems and B est Constants in Approximation Theory","authors":"I. G. Michael","doi":"10.1201/9780429123610-11","DOIUrl":"https://doi.org/10.1201/9780429123610-11","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125601991","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":"Optimization Problems in Fair Division Theory","authors":"M. Dall’Aglio","doi":"10.1201/9780429123610-20","DOIUrl":"https://doi.org/10.1201/9780429123610-20","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125169992","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":"Biorthogonal Local Trigonometric Bases","authors":"J. D. L. Cal, A. M. Valle","doi":"10.1201/9780429123610-14","DOIUrl":"https://doi.org/10.1201/9780429123610-14","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125328780","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":"Midpoint-Type Rules from an Inequalities Point of View","authors":"P. Cerone, S. Dragomir","doi":"10.1201/9780429123610-4","DOIUrl":"https://doi.org/10.1201/9780429123610-4","url":null,"abstract":"The article investigates interior point rules which contain the midpoint as a special case, and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. Thus the simplest open Newton-Cotes rules are examined. Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms. Perturbed quadrature rules are obtained through the use of Gruss, Chebychev and Lupas inequalities, producing a variety of tighter bounds. The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed. The analysis allows the determination of the partition required that would assure that the accuracy the result would be within a prescribed error tolerance. It is demonstrated that the bounds of the approximations are equivalent to those obtained from a Peano kernel that produces Trapezoidal type rules.","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115548689","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":"Pólya-Type Inequalities","authors":"C. Pearce, J. Pečarić, S. Varošanec","doi":"10.1201/9780429123610-10","DOIUrl":"https://doi.org/10.1201/9780429123610-10","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129446070","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":"On Scattered Data Representations Using Bivariate Splines","authors":"D. Hong","doi":"10.1201/9781420036053.CH22","DOIUrl":"https://doi.org/10.1201/9781420036053.CH22","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115379429","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":"Digitized PDE Method for Data Restoration","authors":"S. Osher, Jerry Shen","doi":"10.1201/9781420036053.CH16","DOIUrl":"https://doi.org/10.1201/9781420036053.CH16","url":null,"abstract":"","PeriodicalId":139586,"journal":{"name":"Handbook of Analytic-Computational Methods in Applied Mathematics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115413447","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}