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12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)最新文献

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Numerical Computation of the Mapping Degree using Computational Homology 基于计算同调的映射度数值计算
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.32
K. Nakakura, S. Murashige
{"title":"Numerical Computation of the Mapping Degree using Computational Homology","authors":"K. Nakakura, S. Murashige","doi":"10.1109/SCAN.2006.32","DOIUrl":"https://doi.org/10.1109/SCAN.2006.32","url":null,"abstract":"This paper describes numerical computation of the mapping degree deg(f, Bd)for a continuous map f : Bd) Rd on the d-dimensional ball Bd where d isin Z and ges2. The mapping degree can be defined using a homomorphism which is induced on homology groups. We propose an efficient method to compute the homomorphism without direct calculation of homology groups, and obtain the mapping degree using computational homology.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134432531","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
Adding Constraints to Situations When, In Addition to Intervals,We Also Have Partial Information about Probabilities 在情况下添加约束，除了间隔，我们也有关于概率的部分信息
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.7
M. Ceberio, V. Kreinovich, G. Xiang, S. Ferson, C. Joslyn
{"title":"Adding Constraints to Situations When, In Addition to Intervals,We Also Have Partial Information about Probabilities","authors":"M. Ceberio, V. Kreinovich, G. Xiang, S. Ferson, C. Joslyn","doi":"10.1109/SCAN.2006.7","DOIUrl":"https://doi.org/10.1109/SCAN.2006.7","url":null,"abstract":"In many practical situations, we need to combine probabilistic and interval uncertainty. For example, we need to 1 A compute statistics like population mean E = 1/n.nSigmai=1xi or population variance V = 1/nnSigmai=1(xi-E)2 in situations when we only know intervals xi of possible value of xi. In this case, it is desirable to compute the range of the corresponding characteristic. Some range computation problems are NP-hard; for these problems, in general, only an enclosure is possible. For other problems, there are efficient algorithms. In many practical situations, we have additional information that can be used as constraints on possible cumulative distribution functions (cdfs). For example, we may know that the actual (unknown) cdf is Gaussian. In this paper, we show that such constraints enable us to drastically narrow down the resulting ranges - and sometimes, transform the originally intractable (NP-hard) computational problem of computing the exact range into an efficiently solvable one. This possibility is illustrated on the simplest example of an NP-problem from interval statistics: the problem of computing the range V of the variance V. We also describe how we can estimate the amount of information under such combined intervals-and-constraints uncertainty.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132799510","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
Fast and Accurate Multi-Argument Interval Evaluation of Polynomials 快速准确的多项式多参数区间求值
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.18
A. Frommer, B. Lang
{"title":"Fast and Accurate Multi-Argument Interval Evaluation of Polynomials","authors":"A. Frommer, B. Lang","doi":"10.1109/SCAN.2006.18","DOIUrl":"https://doi.org/10.1109/SCAN.2006.18","url":null,"abstract":"The verification of the existence of certain spherical t- designs involves the evaluation of a degree-t polynomial Jt at a very large number of (interval) arguments. To make the overall verification process feasible computationally, this evaluation must be fast, and the enclosures for the function values must be affected with only modest over-estimation. We discuss several approaches for multi-argument interval evaluation of the polynomial Jt and show how they can be adapted to other polynomials p. One particularly effective new method is based on expanding the polynomial p around several points xij and truncating each resulting expansion PepsivJ to a lower-degree polynomial.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114822173","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: 3
Guaranteed Robust Tracking with Flatness Based Controllers Applying Interval Methods 基于平面度控制器的区间鲁棒跟踪
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.22
M. Kletting, E. Hofer, F. Antritter
{"title":"Guaranteed Robust Tracking with Flatness Based Controllers Applying Interval Methods","authors":"M. Kletting, E. Hofer, F. Antritter","doi":"10.1109/SCAN.2006.22","DOIUrl":"https://doi.org/10.1109/SCAN.2006.22","url":null,"abstract":"Flatness based tracking controller design (see e.g. [4, 5, 16]) is one of the most important tools for the control of nonlinear systems. A drawback of this approach is the lack of methods for the robustness analysis of such controllers with respect to uncertain parameters in the plant. In [1] the application of interval methods has been proposed for the guaranteed robustness analysis of flatness based tracking controllers. This approach allows to explicitly calculate the deviations from the reference trajectory which are caused by uncertain parameters in the plant in a guaranteed way. In this contribution the analysis using interval methods is extended to the case when a nonlinear tracking observer is necessary to estimate unmeasured states. Furthermore it is shown that unknown sensor offsets can be included into this robustness framework. The approach is illustrated for a magnetic levitation system.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130106561","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
Interval Fuzzy Rule-Based Hand Gesture Recognition 基于区间模糊规则的手势识别
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.25
B. Bedregal, G. Dimuro, Antônio R. Costa
{"title":"Interval Fuzzy Rule-Based Hand Gesture Recognition","authors":"B. Bedregal, G. Dimuro, Antônio R. Costa","doi":"10.1109/SCAN.2006.25","DOIUrl":"https://doi.org/10.1109/SCAN.2006.25","url":null,"abstract":"This paper introduces an interval fuzzy rule-based method for the recognition of hand gestures acquired from a data glove, with an application to the recognition of hand gestures of the Brazilian Sign Language. To deal with the uncertainties in the data provided by the data glove, an approach based on interval fuzzy logic is used. The method uses the set of angles of finger joints and of separation between finger for the classification of hand configurations, and classifications of segments of hand gestures for recognizing gestures. The segmentation of gestures is based on the concept of monotonic gesture segment, sequences of hand configurations in which the variations of the angles of the finger joints have the same sign (non-increasing or non-decreasing), separated by reference configurations that mark the inflexion points in the sequence. Each gesture is characterized by its list of monotonic segments. The set of all lists of segments of a given set of gestures determines a set of finite automata able to recognize such gestures.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132668745","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: 24
Vectorised/Semi-Parallel Interval Multiplication 向量化/半并行区间乘法
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.49
E. Malins, M. Szularz, B. Scotney
{"title":"Vectorised/Semi-Parallel Interval Multiplication","authors":"E. Malins, M. Szularz, B. Scotney","doi":"10.1109/SCAN.2006.49","DOIUrl":"https://doi.org/10.1109/SCAN.2006.49","url":null,"abstract":"To date, two principle methods for the multiplication of two intervals have been proposed. Namely, the multiplication of all four bounds and finding their minima/maxima; or by pre-processing the bounds and determining which multiplicands to use based upon their signs. In either case, a minimum of four multiplications are required for complete coverage and special cases such as [0, 1] times [-infin, 1] can result in the less than enlightening [-infin, +infin]. This paper describes a new method of interval multiplication that never requires more than two multiplications, has no special cases and elegantly handles the above case. We continue by describing reformulations of the brute-force and 9-case methods which, through making use of SIMD technology, parallelise and vectorise their operation, ultimately allowing the complete removal of branching. We conclude with an analysis of the algorithms and their performance, compared with the two forementioned traditional techniques.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124357962","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
Interval Techniques for Design of Optimal and Robust Control Strategies 最优鲁棒控制策略设计的区间技术
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.27
A. Rauh, J. Minisini, E. Hofer
{"title":"Interval Techniques for Design of Optimal and Robust Control Strategies","authors":"A. Rauh, J. Minisini, E. Hofer","doi":"10.1109/SCAN.2006.27","DOIUrl":"https://doi.org/10.1109/SCAN.2006.27","url":null,"abstract":"In this paper, an interval arithmetic optimization procedure for both discrete-time and continuous-time systems is presented. Besides computation of control strategies for systems with nominal parameters, robustness requirements for systems with interval bounded uncertainties are considered. Considering these uncertainties, control laws are obtained which directly take into account the influence of disturbances and deviations of system parameters from their nominal values. Compared to Bellman's discrete dynamic programming, errors resulting from gridding of state and control variable intervals as well as errors due to rounding to nearest grid points are avoided. Furthermore, the influence of time discretization errors is taken into account by validated integration of continuous-time state equations. Optimization results for a simplified model of a mechanical positioning system with switchings between models for both static and sliding friction demonstrate the efficiency of the suggested approach and its applicability to processes with state-dependent switching characteristics.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134445418","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: 12
Rigorous lower bounds for the topological entropy via a verified optimization technique 通过验证优化技术得到拓扑熵的严格下界
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.39
B. Bánhelyi, T. Csendes, B. Garay
{"title":"Rigorous lower bounds for the topological entropy via a verified optimization technique","authors":"B. Bánhelyi, T. Csendes, B. Garay","doi":"10.1109/SCAN.2006.39","DOIUrl":"https://doi.org/10.1109/SCAN.2006.39","url":null,"abstract":"Our automatic method developed for the detection of chaos is used for finding rigorous lower bounds for the topological entropy of the classical Henon mapping. We do this within the abstract framework created by Galias and Zgliczynski in 2001, and focus on covering graphs involving different iterations. Our results are compared to those obtained by them.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126899093","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
Analyzing Properties of Fuzzy Implications Obtained via the Interval Constructor 区间构造函数模糊含义的性质分析
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.5540/TEMA.2007.08.01.0033
B. Bedregal, R. Santiago, R. Reiser, G. Dimuro
{"title":"Analyzing Properties of Fuzzy Implications Obtained via the Interval Constructor","authors":"B. Bedregal, R. Santiago, R. Reiser, G. Dimuro","doi":"10.5540/TEMA.2007.08.01.0033","DOIUrl":"https://doi.org/10.5540/TEMA.2007.08.01.0033","url":null,"abstract":"This work considers an interval extension of fuzzy implications based on the best interval representation of usual fuzzy implications. The related properties of fuzzy implications can be naturally extended and the interval representation meets the optimality property and preserves the behaviors of the implications in the interval endpoints. Our discussion mainly focuses on the best interval representation of three important classes of fuzzy implications: S-implications, R-implications and QL-implications. We analyze sufficient and necessary conditions for these three classes of implications as inclusion-monotonic functions in both arguments satisfying the minimal properties of fuzzy implications.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128119855","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: 16
Rigorous Inner Approximation of the Range of Functions 函数范围的严格内逼近
12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-26 DOI: 10.1109/SCAN.2006.38
A. Goldsztejn, W. Hayes
{"title":"Rigorous Inner Approximation of the Range of Functions","authors":"A. Goldsztejn, W. Hayes","doi":"10.1109/SCAN.2006.38","DOIUrl":"https://doi.org/10.1109/SCAN.2006.38","url":null,"abstract":"A basic problem of interval analysis is the computation of a superset of the image of an interval by a function, called an outer enclosure. Here we consider the computation of an inner enclosure, which is a subset of the image. Inner approximations are harder than the outer ones in general: proving that a box is inside the image is equivalent to proving existence of solutions for a collection of systems of equations. Based on this remark, a new construction of the inner approximation is proposed that is particularly efficient for small domains. Then, it is shown than one can apply these ideas in the context of ordinary differential equations, hence providing some tools of potential interest for the theory of shadowing in dynamical systems.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131761594","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: 4
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