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Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problems 混合拉普拉斯特征值问题的BDM有限元逼近的渐近精确后验误差估计
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-05-22 DOI: 10.1007/s10543-023-00976-w
P. Lederer
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引用次数: 0
Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-p base $$beta $$ 以precision-p为基数计算第一个单位(ufp)和最后一个单位(ulp) $$beta $$
3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-29 DOI: 10.1007/s10543-023-00970-2
Siegfried M. Rump
{"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}
引用次数: 0
Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package 构建Rosenbrock-Wanner方法Rodas5P和Julia微分方程包内的数值基准
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-17 DOI: 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}
引用次数: 3
On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation 非线性狄拉克方程半非相对论性极限系统的数值方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-13 DOI: 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}
引用次数: 0
Proximal gradient algorithm for nonconvex low tubal rank tensor recovery 非凸低阶张量恢复的近端梯度算法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-04 DOI: 10.1007/s10543-023-00964-0
Yanhui Liu, Xueying Zeng, Weiguo Wang
{"title":"Proximal gradient algorithm for nonconvex low tubal rank tensor recovery","authors":"Yanhui Liu, Xueying Zeng, Weiguo Wang","doi":"10.1007/s10543-023-00964-0","DOIUrl":"https://doi.org/10.1007/s10543-023-00964-0","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44004635","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}
引用次数: 0
Product integration rules by the constrained mock-Chebyshev least squares operator 约束mock Chebyshev最小二乘算子的乘积积分规则
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-04-03 DOI: 10.1007/s10543-023-00968-w
F. Dell’Accio, Domenico Mezzanotte, Federico Nudo, D. Occorsio
{"title":"Product integration rules by the constrained mock-Chebyshev least squares operator","authors":"F. Dell’Accio, Domenico Mezzanotte, Federico Nudo, D. Occorsio","doi":"10.1007/s10543-023-00968-w","DOIUrl":"https://doi.org/10.1007/s10543-023-00968-w","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43029450","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}
引用次数: 0
Low cardinality positive interior cubature on NURBS-shaped domains nurbs形域上的低基数正内培养
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-03-17 DOI: 10.1007/s10543-023-00958-y
A. Sommariva, M. Vianello
{"title":"Low cardinality positive interior cubature on NURBS-shaped domains","authors":"A. Sommariva, M. Vianello","doi":"10.1007/s10543-023-00958-y","DOIUrl":"https://doi.org/10.1007/s10543-023-00958-y","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"65 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51984138","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}
引用次数: 7
An Hermite-Obreschkoff method for stiff high-index DAE 一种求解刚性高指数DAE的Hermite-Obreschkoff方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-02-18 DOI: 10.1007/s10543-023-00955-1
R. Zolfaghari, N. Nedialkov
{"title":"An Hermite-Obreschkoff method for stiff high-index DAE","authors":"R. Zolfaghari, N. Nedialkov","doi":"10.1007/s10543-023-00955-1","DOIUrl":"https://doi.org/10.1007/s10543-023-00955-1","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":" ","pages":"1-29"},"PeriodicalIF":1.5,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42419826","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}
引用次数: 1
On the order reduction of approximations of fractional derivatives: an explanation and a cure 关于分数导数近似的降阶：一种解释和解决方法
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-02-12 DOI: 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}
引用次数: 0
Small time chaos approximations for heat kernels of multidimensional diffusions 多维扩散热核的小时间混沌近似
IF 1.5 3区 数学
BIT Numerical Mathematics Pub Date : 2023-02-12 DOI: 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}
引用次数: 0
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