Reliable Computing最新文献

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Dear colleagues 亲爱的同事们
Reliable Computing Pub Date : 2021-12-04 DOI: 10.1007/BF02384049
V. Nesterov
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引用次数: 0
A Rigorous Extension of the Schönhage-Strassen Integer Multiplication Algorithm Using Complex Interval Arithmetic 用复区间算法对Schönhage-Strassen整数乘法算法的严格扩展
Reliable Computing Pub Date : 2010-06-01 DOI: 10.4204/EPTCS.24.19
R. Sainudiin, T. Steinke
{"title":"A Rigorous Extension of the Schönhage-Strassen Integer Multiplication Algorithm Using Complex Interval Arithmetic","authors":"R. Sainudiin, T. Steinke","doi":"10.4204/EPTCS.24.19","DOIUrl":"https://doi.org/10.4204/EPTCS.24.19","url":null,"abstract":"Multiplication of n-digit integers by long multiplication requires O(n 2 ) operations and can be time-consuming. A. Schonhage and V. Strassen published an algorithm in 1970 that is capable of performing the task with only O(nlog(n)) arithmetic operations over C; naturally, finite-precision approximations to C are used and rounding errors need to be accounted for. Overall, using variable-precision fixed-point numbers, this results in an O(n(log(n)) 2+\" )-time algorithm. However, to make this algorithm more efficient and practical we need to make use of hardware-based floating- point numbers. How do we deal with rounding errors? and how do we determine the limits of the fixed-precision hardware? Our solution is to use interval arithmetic to guarantee the correctness of results and deter- mine the hardware's limits. We examine the feasibility of this approach and are able to report that 75,000-digit base-256 integers can be han- dled using double-precision containment sets. This demonstrates that our approach has practical potential; however, at this stage, our implemen- tation does not yet compete with commercial ones, but we are able to demonstrate the feasibility of this technique.","PeriodicalId":54499,"journal":{"name":"Reliable Computing","volume":"41 1","pages":"151-159"},"PeriodicalIF":0.0,"publicationDate":"2010-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82675247","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
Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms 区间不确定性下计算总体方差和熵:线性时间算法
Reliable Computing Pub Date : 2007-12-01 DOI: 10.1007/s11155-007-9045-6
G. Xiang, M. Ceberio, V. Kreinovich
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引用次数: 28
Determining the Positive Definiteness Margin of Interval Matrices 区间矩阵正定边的确定
Reliable Computing Pub Date : 2007-12-01 DOI: 10.1007/s11155-007-9046-5
L. Kolev
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引用次数: 6
Computing the Pessimism of Inclusion Functions 计算包含函数的悲观主义
Reliable Computing Pub Date : 2007-12-01 DOI: 10.1007/s11155-007-9044-7
G. Chabert, L. Jaulin
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引用次数: 6
Guaranteeing the Homotopy Type of a Set Defined by Non-Linear Inequalities 保证由非线性不等式定义的集合的同伦类型
Reliable Computing Pub Date : 2007-09-19 DOI: 10.1007/s11155-007-9043-8
N. Delanoue, L. Jaulin, Bertrand Cottenceau
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引用次数: 10
Optimal Multiplication of G-intervals g区间的最优乘法
Reliable Computing Pub Date : 2007-09-19 DOI: 10.1007/s11155-007-9041-x
L. Kolev
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引用次数: 10
On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis 关于注入性的充分条件:基于区间分析的数值测试算法的发展
Reliable Computing Pub Date : 2007-09-19 DOI: 10.1007/S11155-007-9042-9
S. Lagrange, N. Delanoue, L. Jaulin
{"title":"On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis","authors":"S. Lagrange, N. Delanoue, L. Jaulin","doi":"10.1007/S11155-007-9042-9","DOIUrl":"https://doi.org/10.1007/S11155-007-9042-9","url":null,"abstract":"","PeriodicalId":54499,"journal":{"name":"Reliable Computing","volume":"13 1","pages":"409-421"},"PeriodicalIF":0.0,"publicationDate":"2007-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11155-007-9042-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53079477","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: 13
An Application of Interval Methods to Stock Market Forecasting 区间方法在股票市场预测中的应用
Reliable Computing Pub Date : 2007-09-19 DOI: 10.1007/s11155-007-9039-4
Chenyi Hu, Ling T. He
{"title":"An Application of Interval Methods to Stock Market Forecasting","authors":"Chenyi Hu, Ling T. He","doi":"10.1007/s11155-007-9039-4","DOIUrl":"https://doi.org/10.1007/s11155-007-9039-4","url":null,"abstract":"","PeriodicalId":54499,"journal":{"name":"Reliable Computing","volume":"13 1","pages":"423-434"},"PeriodicalIF":0.0,"publicationDate":"2007-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11155-007-9039-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53079840","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: 58
Interval-Related Talks at the North American Fuzzy Information Processing Society Annual Conference NAFIPS’07 北美模糊信息处理学会年会(NAFIPS ' 07)间隙相关演讲
Reliable Computing Pub Date : 2007-09-18 DOI: 10.1007/s11155-007-9038-5
O. Castillo, V. Kreinovich
{"title":"Interval-Related Talks at the North American Fuzzy Information Processing Society Annual Conference NAFIPS’07","authors":"O. Castillo, V. Kreinovich","doi":"10.1007/s11155-007-9038-5","DOIUrl":"https://doi.org/10.1007/s11155-007-9038-5","url":null,"abstract":"","PeriodicalId":54499,"journal":{"name":"Reliable Computing","volume":"13 1","pages":"441-443"},"PeriodicalIF":0.0,"publicationDate":"2007-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11155-007-9038-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53079832","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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