Pub Date : 1900-01-01DOI: 10.1142/9789812836267_0005
K. Atkinson
This is a personal perspective on the development of numerical methods for solving Fredholm integral equations of the second kind, discussing work being done principally during the 1950s and 1960s. The principal types of numerical methods being studied were projection methods (Galerkin, collocation) and Nystrom methods. During the 1950s and 1960s, functional analysis became the framework for the analysis of numerical methods for solving integral equations, and this inuenced the questions being asked. This paper looks at the history of the analyses being done at that time.
{"title":"A personal perspective on the history of the numerical analysis of Fredholm integral equations of the second kind","authors":"K. Atkinson","doi":"10.1142/9789812836267_0005","DOIUrl":"https://doi.org/10.1142/9789812836267_0005","url":null,"abstract":"This is a personal perspective on the development of numerical methods for solving Fredholm integral equations of the second kind, discussing work being done principally during the 1950s and 1960s. The principal types of numerical methods being studied were projection methods (Galerkin, collocation) and Nystrom methods. During the 1950s and 1960s, functional analysis became the framework for the analysis of numerical methods for solving integral equations, and this inuenced the questions being asked. This paper looks at the history of the analyses being done at that time.","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"76 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":"131506698","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: 10.1142/9789812836267_0006
B. Ford
{"title":"Memoires on building a general purpose numerical algorithms library","authors":"B. Ford","doi":"10.1142/9789812836267_0006","DOIUrl":"https://doi.org/10.1142/9789812836267_0006","url":null,"abstract":"","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"65 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":"114544637","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: 10.1142/9789812836267_0003
J. Butcher
Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved "by hand" and require the use of numerical methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations.
{"title":"Numerical methods for ordinary differential equations: early days","authors":"J. Butcher","doi":"10.1142/9789812836267_0003","DOIUrl":"https://doi.org/10.1142/9789812836267_0003","url":null,"abstract":"Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved \"by hand\" and require the use of numerical methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations.","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"78 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":"124503287","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: 10.1142/9789812836267_0013
R. Piessens
{"title":"Applications of Chebyshev polynomials: from theoretical kinematics to practical computations","authors":"R. Piessens","doi":"10.1142/9789812836267_0013","DOIUrl":"https://doi.org/10.1142/9789812836267_0013","url":null,"abstract":"","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"21 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":"123833683","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: 10.1142/9789812836267_0007
J. Dongarra, H. Meuer, H. Simon, E. Strohmaier
{"title":"Recent trends in high performance computing","authors":"J. Dongarra, H. Meuer, H. Simon, E. Strohmaier","doi":"10.1142/9789812836267_0007","DOIUrl":"https://doi.org/10.1142/9789812836267_0007","url":null,"abstract":"","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"197 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":"115663705","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: 10.1142/9789812836267_0012
P. Davis
{"title":"My early experiences with scientific computation","authors":"P. Davis","doi":"10.1142/9789812836267_0012","DOIUrl":"https://doi.org/10.1142/9789812836267_0012","url":null,"abstract":"","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"28 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":"116986334","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: 10.1142/9789812836267_0008
Donghui Chen, R. Plemmons
A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given. Special emphasis is placed on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization. Techniques involving nonnegative low-rank matrix and tensor factorizations are also emphasized. Details are provided for some important classical and modern applications in science and engineering. For completeness, this report also includes an effort toward a literature survey of the various algorithms and applications of nonnegativity constraints in numerical analysis.
{"title":"Nonnegativity constraints in numerical analysis","authors":"Donghui Chen, R. Plemmons","doi":"10.1142/9789812836267_0008","DOIUrl":"https://doi.org/10.1142/9789812836267_0008","url":null,"abstract":"A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given. Special emphasis is placed on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization. Techniques involving nonnegative low-rank matrix and tensor factorizations are also emphasized. Details are provided for some important classical and modern applications in science and engineering. For completeness, this report also includes an effort toward a literature survey of the various algorithms and applications of nonnegativity constraints in numerical analysis.","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"51 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":"127425361","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：