Math. Comput. Model.最新文献

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Stability of finite difference schemes approximation for hyperbolic boundary value problems in an interval 区间内双曲型边值问题有限差分格式逼近的稳定性
Math. Comput. Model. Pub Date : 2021-09-15 DOI: 10.1090/mcom/3698
Antoine Benoit
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引用次数: 1
A classification of ECM-friendly families of elliptic curves using modular curves 用模曲线对椭圆曲线族的ecm友好分类
Math. Comput. Model. Pub Date : 2021-09-15 DOI: 10.1090/mcom/3697
R. Barbulescu, Sudarshan Shinde
{"title":"A classification of ECM-friendly families of elliptic curves using modular curves","authors":"R. Barbulescu, Sudarshan Shinde","doi":"10.1090/mcom/3697","DOIUrl":"https://doi.org/10.1090/mcom/3697","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"15 1","pages":"1405-1436"},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75587379","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}
引用次数: 2
On bounds for Kummer's function ratio 关于Kummer函数比值的界
Math. Comput. Model. Pub Date : 2021-09-14 DOI: 10.1090/mcom/3690
Lukas Sablica, K. Hornik
{"title":"On bounds for Kummer's function ratio","authors":"Lukas Sablica, K. Hornik","doi":"10.1090/mcom/3690","DOIUrl":"https://doi.org/10.1090/mcom/3690","url":null,"abstract":"Summary: In this paper we present lower and upper bounds for Kummer’s function ratios of the form M ( a,b,z ) ′ M ( a,b,z ) when 0 < a < b . The derived bounds are asymptotically precise, theoretically well-defined, numerically accurate, and easy to compute. Moreover, we show how the bounds can be used as starting values for monotonically convergent sequences to approximate the ratio with even higher precision while avoiding the anomalous convergence discussed by Gautschi [Math. Comp. 31 (1977), pp. 994-999]. This allows to apply the results in multiple areas, as for example the estimation of Watson distributions in statistical modelling. Furthermore, we extend the convergence results provided by Gautschi and the list of known bounds for the inverse of Kummer’s function ratio given by Sra and Karp [J. Multivariate Anal. 114 (2013), pp. 256-269]. In addition, the derived starting bounds are compared and connected to other results from the literature.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"102 1","pages":"887-907"},"PeriodicalIF":0.0,"publicationDate":"2021-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85518546","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}
引用次数: 1
Stability and error analysis for a second-order approximation of 1D nonlocal Schrödinger equation under DtN-type boundary conditions dtn型边界条件下一维非局部Schrödinger方程二阶近似的稳定性与误差分析
Math. Comput. Model. Pub Date : 2021-09-10 DOI: 10.1090/mcom/3685
Jihong Wang, Jiwei Zhang, Chunxiong Zheng
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引用次数: 6
New results for witnesses of Robin's criterion 罗宾标准的证人的新结果
Math. Comput. Model. Pub Date : 2021-09-04 DOI: 10.1090/mcom/3687
Y. Saouter
{"title":"New results for witnesses of Robin's criterion","authors":"Y. Saouter","doi":"10.1090/mcom/3687","DOIUrl":"https://doi.org/10.1090/mcom/3687","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"14 1","pages":"909-920"},"PeriodicalIF":0.0,"publicationDate":"2021-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72772009","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}
引用次数: 0
On the q-analogue of the Pair Correlation Conjecture via Fourier optimization 基于傅里叶优化的对相关猜想的q-模拟
Math. Comput. Model. Pub Date : 2021-08-23 DOI: 10.1090/mcom/3747
Oscar E. Quesada-Herrera
{"title":"On the q-analogue of the Pair Correlation Conjecture via Fourier optimization","authors":"Oscar E. Quesada-Herrera","doi":"10.1090/mcom/3747","DOIUrl":"https://doi.org/10.1090/mcom/3747","url":null,"abstract":"We study the $q$-analogue of the average of Montgomery's function $F(alpha, T)$ over bounded intervals. Assuming the Generalized Riemann Hypothesis for Dirichlet $L$-functions, we obtain upper and lower bounds for this average over an interval that are quite close to the pointwise conjectured value of 1. To compute our bounds, we extend a Fourier analysis approach by Carneiro, Chandee, Chirre, and Milinovich, and apply computational methods of non-smooth programming.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"5 1","pages":"2347-2365"},"PeriodicalIF":0.0,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75177861","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}
引用次数: 1
Nitsche's method for Navier-Stokes equations with slip boundary conditions 带滑移边界条件的Navier-Stokes方程的Nitsche方法
Math. Comput. Model. Pub Date : 2021-08-10 DOI: 10.1090/mcom/3682
I. Gjerde, L. Scott
{"title":"Nitsche's method for Navier-Stokes equations with slip boundary conditions","authors":"I. Gjerde, L. Scott","doi":"10.1090/mcom/3682","DOIUrl":"https://doi.org/10.1090/mcom/3682","url":null,"abstract":"","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"104 1","pages":"597-622"},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73736900","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}
引用次数: 11
Recovery of Sobolev functions restricted to iid sampling 限定采样的Sobolev函数的恢复
Math. Comput. Model. Pub Date : 2021-08-04 DOI: 10.1090/mcom/3763
David Krieg, E. Novak, Mathias Sonnleitner
{"title":"Recovery of Sobolev functions restricted to iid sampling","authors":"David Krieg, E. Novak, Mathias Sonnleitner","doi":"10.1090/mcom/3763","DOIUrl":"https://doi.org/10.1090/mcom/3763","url":null,"abstract":"We study Lq-approximation and integration for functions from the Sobolev space W s p (Ω) and compare optimal randomized (Monte Carlo) algorithms with algorithms that can only use iid sample points, uniformly distributed on the domain. The main result is that we obtain the same optimal rate of convergence if we restrict to iid sampling, a common assumption in learning and uncertainty quantification. The only exception is when p = q = ∞, where a logarithmic loss cannot be avoided.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"10 5 1","pages":"2715-2738"},"PeriodicalIF":0.0,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75933849","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}
引用次数: 6
Computing p-adic L-functions of totally real fields 计算全实域的p进l函数
Math. Comput. Model. Pub Date : 2021-06-26 DOI: 10.1090/mcom/3678
Jan Vonk, Contents
{"title":"Computing p-adic L-functions of totally real fields","authors":"Jan Vonk, Contents","doi":"10.1090/mcom/3678","DOIUrl":"https://doi.org/10.1090/mcom/3678","url":null,"abstract":"We describe an algorithm for computing p-adic L-functions of characters of totally real elds. Such p-adic L-functions were constructed in the 1970’s independently by Barsky and CassouNoguès [Bar78, CN79] based on the explicit formula for zeta values of Shintani [Shi76] and by Serre and Deligne–Ribet [Ser73, DR80] using Hilbert modular forms and an idea of Siegel [Sie68] going back to Hecke [Hec24, Satz 3]. An algorithm for computing via the approach of Cassou-Noguès was developed by Roblot1 [Rob15]. Our algorithm follows the approach of Serre and Siegel, and its computational e ciency rests upon a method for computing with p-adic spaces of modular forms developed in previous work by the authors. The idea of our method is simple. In Serre’s approach, the value of the p-adic L-function of a totally real eld of degree d at a non-positive integer 1 − k is interpreted as the constant term of a classical modular form of weight dk obtained by diagonally restricting a Hilbert Eisenstein series. For small values of k these constants can be computed easily using an idea of Siegel, which goes back to Hecke. To compute the p-adic L-function at arbitrary points in its domain, to some nite p-adic precision, we use a method for computing p-adically with modular forms in larger weight developed in [Lau11, Von15]. We compute the required constant term in very large weight indirectly, by nding su ciently many of its higher Fourier coe cients and using linear algebra to deduce the unknown constant term. Thus our approach is an algorithmic incarnation of Serre’s approach to p-adic L-functions of totally real elds [Ser73], obtaining p-adic congruences between the constant terms of modular forms by studying their higher Fourier coe cients.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"9 1","pages":"921-942"},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74501495","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}
引用次数: 7
Corrigendum to "On two classes of simultaneous Pell equations with no solutions" “关于两类无解的联立Pell方程”的勘误
Math. Comput. Model. Pub Date : 2021-06-23 DOI: 10.1090/MCOM/3677
P. Walsh
{"title":"Corrigendum to \"On two classes of simultaneous Pell equations with no solutions\"","authors":"P. Walsh","doi":"10.1090/MCOM/3677","DOIUrl":"https://doi.org/10.1090/MCOM/3677","url":null,"abstract":"In this short note, we identify an error made in an earlier paper [Math. Comp. 68 (1999), no. 225, pp. 385–388] on simultaneous Pell equations, provide a revised statement of the main results contained therein, and show how this modification lends itself to the correctness of the proofs given in the earlier paper.","PeriodicalId":18301,"journal":{"name":"Math. Comput. Model.","volume":"18 1","pages":"2503-2505"},"PeriodicalIF":0.0,"publicationDate":"2021-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86855895","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}
引用次数: 0
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