März 1981Pub Date : 1981-12-31DOI: 10.1002/ZAMM.19810610304
H. E. Salzer
{"title":"Rational Interpolation Using Incomplete Barycentric Forms","authors":"H. E. Salzer","doi":"10.1002/ZAMM.19810610304","DOIUrl":"https://doi.org/10.1002/ZAMM.19810610304","url":null,"abstract":"In rational interpolation of ƒ(x) by (a0 + a1x + … + anxn)/(1 + b1x + … + bmxm) at xi, i = 1(1)n + m + 1, instead of solving an (n + m + 1)-th order linear system for ai and bi, we solve only an m-th order linear system to obtain all n + m + 1 coefficients of 1/(x - xi) in the “incomplete barycentric form” of the numerator and denominator. The extension to r-th order osculatory interpolation by (a0 + a1x + … + anr - 1xnr - 1)/(1 + b1x + … + bmrxmr) requires the solution of an rm-th, instead of the usual (rm + rn)-th order linear system. In similar treatment of non-osculatory odd-point rational trigonometric interpolation by a quotient of trigonometric sums, we solve a 2m-th, instead of (2n + 2m + 1)-th order linear system for the coefficients of 1/sin 1/2 (x - xi). \u0000 \u0000 \u0000 \u0000Bei der rationalen Interpolation von ƒ(x) durch (a0 + a1x + … + anxn)/(1 + b1x + … + bmxm) in xi, i = 1(1) n + m + 1 losen wir anstatt eines linearen Systems (n + m + 1)-ter Ordnung Fur ai und bi nur ein System m-ter Ordnung, um samtliche Koeffizienten von 1/(x - xi) in der „unvollstandigen baryzentrischen Form” von Zahler und Nenner zu erhalten. Die Ausdehnung auf osculatorische Interpolation r-ter Ordnung durch (a0 + a1x + … + anr - 1xnr - 1)/(1 + b1x + … + bmrxmr) erfordert die Losung eines Systems rm-ter Ordnung anstelle des gewohnlichen linearen Systems (rm + rn)-ter Ordnung. In ahnlicher Behandlung nicht-osculatorischer rationaler trigonometrischer Interpolation uber eine ungerade Punktanzahl durch den Quotienten trigonometrischer Summen losen wir ein lineares System 2m-ter anstelle (2n + 2m + 1)-ter Ordnung Fur die Koeffizienten von 1/sin 1/2 (x - xi).","PeriodicalId":193012,"journal":{"name":"März 1981","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128529831","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}
März 1981Pub Date : 1981-12-31DOI: 10.1515/9783112524121-011
A. Chyliński, T. Radoszewski
{"title":"4π(α, β)-γ Two-Stage Coincidence Method with Liquid Scintillation Counter in α, β-Channel for Absolute Determination of Radioactive Concentration","authors":"A. Chyliński, T. Radoszewski","doi":"10.1515/9783112524121-011","DOIUrl":"https://doi.org/10.1515/9783112524121-011","url":null,"abstract":"","PeriodicalId":193012,"journal":{"name":"März 1981","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134351768","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}
März 1981Pub Date : 1981-12-31DOI: 10.1002/ZAMM.19810610309
N. Anderson, A. Arthurs
{"title":"Variational Solution of a Nonlinear Boundary Value Problem in the Theory of Power Law Fluids","authors":"N. Anderson, A. Arthurs","doi":"10.1002/ZAMM.19810610309","DOIUrl":"https://doi.org/10.1002/ZAMM.19810610309","url":null,"abstract":"","PeriodicalId":193012,"journal":{"name":"März 1981","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121276417","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}