Pub Date : 2023-05-22DOI: 10.1007/s10543-023-00976-w
P. Lederer
{"title":"Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems","authors":"P. Lederer","doi":"10.1007/s10543-023-00976-w","DOIUrl":"https://doi.org/10.1007/s10543-023-00976-w","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-29DOI: 10.1007/s10543-023-00970-2
Siegfried M. Rump
Abstract There are simple algorithms to compute the predecessor, successor, unit in the first place, unit in the last place etc. in binary arithmetic. In this note equally simple algorithms for computing the unit in the first place and the unit in the last place in precision- p base- $$beta $$ β arithmetic with $$p geqslant 1$$ p⩾1 and with $$beta geqslant 2$$ β⩾2 are presented. The algorithms work in the underflow range, and numbers close to overflow are treated by scaling. The algorithms use only the basic operations with directed rounding. If the successor (or predecessor) of a floating-point number is available, an algorithm in rounding to nearest is presented as well.
{"title":"Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$beta $$","authors":"Siegfried M. Rump","doi":"10.1007/s10543-023-00970-2","DOIUrl":"https://doi.org/10.1007/s10543-023-00970-2","url":null,"abstract":"Abstract There are simple algorithms to compute the predecessor, successor, unit in the first place, unit in the last place etc. in binary arithmetic. In this note equally simple algorithms for computing the unit in the first place and the unit in the last place in precision- p base- $$beta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>β</mml:mi> </mml:math> arithmetic with $$p geqslant 1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and with $$beta geqslant 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> are presented. The algorithms work in the underflow range, and numbers close to overflow are treated by scaling. The algorithms use only the basic operations with directed rounding. If the successor (or predecessor) of a floating-point number is available, an algorithm in rounding to nearest is presented as well.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"195 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135802277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-17DOI: 10.1007/s10543-023-00967-x
G. Steinebach
{"title":"Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package","authors":"G. Steinebach","doi":"10.1007/s10543-023-00967-x","DOIUrl":"https://doi.org/10.1007/s10543-023-00967-x","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-26"},"PeriodicalIF":1.5,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41772404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-13DOI: 10.1007/s10543-023-00971-1
T. Jahnke, Michael Kirn
{"title":"On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation","authors":"T. Jahnke, Michael Kirn","doi":"10.1007/s10543-023-00971-1","DOIUrl":"https://doi.org/10.1007/s10543-023-00971-1","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43185375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-12DOI: 10.1007/s10543-023-00961-3
B. Jacobs, Fredrik Laurén, J. Nordström
{"title":"On the order reduction of approximations of fractional derivatives: an explanation and a cure","authors":"B. Jacobs, Fredrik Laurén, J. Nordström","doi":"10.1007/s10543-023-00961-3","DOIUrl":"https://doi.org/10.1007/s10543-023-00961-3","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-14"},"PeriodicalIF":1.5,"publicationDate":"2023-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41482503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-12DOI: 10.1007/s10543-023-00949-z
D. Ivanenko, A. Kohatsu-Higa, A. Kulik
{"title":"Small time chaos approximations for heat kernels of multidimensional diffusions","authors":"D. Ivanenko, A. Kohatsu-Higa, A. Kulik","doi":"10.1007/s10543-023-00949-z","DOIUrl":"https://doi.org/10.1007/s10543-023-00949-z","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-34"},"PeriodicalIF":1.5,"publicationDate":"2023-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44920629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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