O. Kosheleva, V. Kreinovich, L. Longpré, Mourat Tschoshanov, G. Xiang
There are many papers that experimentally compare effectiveness of different teaching techniques. Most of these papers use traditional statistical approach to process the experimental results. The traditional statistical approach is well suited to numerical data but often, what we are processing is intervals (e.g., a means anything from 90 to 100). We show that the use of interval techniques leads to more adequate processing of educational data.
{"title":"Towards Interval Techniques for Processing Educational Data","authors":"O. Kosheleva, V. Kreinovich, L. Longpré, Mourat Tschoshanov, G. Xiang","doi":"10.1109/SCAN.2006.46","DOIUrl":"https://doi.org/10.1109/SCAN.2006.46","url":null,"abstract":"There are many papers that experimentally compare effectiveness of different teaching techniques. Most of these papers use traditional statistical approach to process the experimental results. The traditional statistical approach is well suited to numerical data but often, what we are processing is intervals (e.g., a means anything from 90 to 100). We show that the use of interval techniques leads to more adequate processing of educational data.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"135 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":"124630814","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}
The authors propose a criterion how to decide a cluster of eigenvalues to be a multiple eigenvalue or nearly multiple eigenvalues in finite precision arithmetic. If the matrix has a multiple eigenvalue, the eigenvector and the generalized ones are computed by their method, and therefore the Jordan canonical form can be derived. Results of numerical experiments for several kinds of matrices are shown.
{"title":"Computing the Jordan canonical form in finite precision arithmetic","authors":"T. Suzuki","doi":"10.1109/SCAN.2006.13","DOIUrl":"https://doi.org/10.1109/SCAN.2006.13","url":null,"abstract":"The authors propose a criterion how to decide a cluster of eigenvalues to be a multiple eigenvalue or nearly multiple eigenvalues in finite precision arithmetic. If the matrix has a multiple eigenvalue, the eigenvector and the generalized ones are computed by their method, and therefore the Jordan canonical form can be derived. Results of numerical experiments for several kinds of matrices are shown.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"52 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":"121997862","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}
We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.
{"title":"Interval Tools for ODEs and DAEs","authors":"N. Nedialkov","doi":"10.1109/SCAN.2006.28","DOIUrl":"https://doi.org/10.1109/SCAN.2006.28","url":null,"abstract":"We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133094904","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}
This paper discusses the problem what makes a computer-assisted proof trustworthy, the quest for an algorithmic support system for computer-assisted proof relations to global optimization, an analysis of some recent proofs, and some current challenges which appear to be amenable to a computer-assisted treatment.
{"title":"Computer-assisted proofs","authors":"Arnold Neumaier","doi":"10.1109/SCAN.2006.11","DOIUrl":"https://doi.org/10.1109/SCAN.2006.11","url":null,"abstract":"This paper discusses the problem what makes a computer-assisted proof trustworthy, the quest for an algorithmic support system for computer-assisted proof relations to global optimization, an analysis of some recent proofs, and some current challenges which appear to be amenable to a computer-assisted treatment.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"28 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114132963","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}
We investigate some algebraic properties of the system of stochastic numbers with the arithmetic operations addition and multiplication by scalars and the relation inclusion and point out certain practically important consequences from these properties. Our idea is to start from a minimal set of empirically known properties and to study these properties by an axiomatic approach. Based on this approach we develop an algebraic theory of stochastic numbers. A numerical example based on the Lagrange polynomial demonstrates the consistency between the CESTAC method and the presented theory of stochastic numbers.
{"title":"On the solution to numerical problems using stochastic arithmetic","authors":"R. Alt, J. Lamotte, S. Markov","doi":"10.1109/SCAN.2006.35","DOIUrl":"https://doi.org/10.1109/SCAN.2006.35","url":null,"abstract":"We investigate some algebraic properties of the system of stochastic numbers with the arithmetic operations addition and multiplication by scalars and the relation inclusion and point out certain practically important consequences from these properties. Our idea is to start from a minimal set of empirically known properties and to study these properties by an axiomatic approach. Based on this approach we develop an algebraic theory of stochastic numbers. A numerical example based on the Lagrange polynomial demonstrates the consistency between the CESTAC method and the presented theory of stochastic numbers.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114313736","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}
This paper addresses the problem of solving parametric linear systems of equations whose coefficients are, in the general case, nonlinear functions of interval parameters. Such systems, are encountered in many practical problems, e.g in electrical engineering and mechanical systems. A C-XSC implementation of a parametric fixed-point iteration method for computing an outer enclosure for the solution set is proposed in this paper. Numerical examples illustrating the applicability of the proposed method are solved, and compared with other methods.
{"title":"Parametric Linear System of Equations, Whose Elements are Nonlinear Functions","authors":"H. El-Owny","doi":"10.1109/SCAN.2006.37","DOIUrl":"https://doi.org/10.1109/SCAN.2006.37","url":null,"abstract":"This paper addresses the problem of solving parametric linear systems of equations whose coefficients are, in the general case, nonlinear functions of interval parameters. Such systems, are encountered in many practical problems, e.g in electrical engineering and mechanical systems. A C-XSC implementation of a parametric fixed-point iteration method for computing an outer enclosure for the solution set is proposed in this paper. Numerical examples illustrating the applicability of the proposed method are solved, and compared with other methods.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"728 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128967394","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}
In this paper, we apply the validated modeling and simulation environment SMARTMOBILE along with two solvers recently added to its core to the problem of the identification of muscle activation in general motor tasks. The identification of muscle activation is one of the important and still open problems in biomechanics which aims at helping physicians assess an individual therapy for a patient. We address the discrepancy of the results supplied by the proposed simplified muscle activation model to the gait lab data and make an initial analysis of model's parameter sensitivity using validated techniques.
{"title":"Toward Validating a Simplified Muscle Activation Model in SMARTMOBILE","authors":"E. Auer, M. Tandl, D. Strobach, A. Kecskeméthy","doi":"10.1109/SCAN.2006.44","DOIUrl":"https://doi.org/10.1109/SCAN.2006.44","url":null,"abstract":"In this paper, we apply the validated modeling and simulation environment SMARTMOBILE along with two solvers recently added to its core to the problem of the identification of muscle activation in general motor tasks. The identification of muscle activation is one of the important and still open problems in biomechanics which aims at helping physicians assess an individual therapy for a patient. We address the discrepancy of the results supplied by the proposed simplified muscle activation model to the gait lab data and make an initial analysis of model's parameter sensitivity using validated techniques.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125375833","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}
The optimization of the functionality and the guarantee of a safe operation of a technical system are important issues in industry. These aspects become even more important when we have to deal with numerous uncertainties which heavily influence the behavior of the technical system under consideration and - in the worst case - cause system failure. Appropriate interval tools can offer solutions to problems where system uncertainties play a key role. Over the recent years at the Institute of Measurement, Control, and Microtechnology existing interval tools have been extended and new modules have been developed. In this contribution, successful applications of interval algorithms to real-world problems in various fields of engineering are presented. The focus is on measuring techniques including interval observers and sensitivity analysis as well as design of optimal and robust controllers for continuous-time and discrete-time systems.
{"title":"Applications of Interval Algorithms in Engineering","authors":"E. Hofer, A. Rauh","doi":"10.1109/SCAN.2006.10","DOIUrl":"https://doi.org/10.1109/SCAN.2006.10","url":null,"abstract":"The optimization of the functionality and the guarantee of a safe operation of a technical system are important issues in industry. These aspects become even more important when we have to deal with numerous uncertainties which heavily influence the behavior of the technical system under consideration and - in the worst case - cause system failure. Appropriate interval tools can offer solutions to problems where system uncertainties play a key role. Over the recent years at the Institute of Measurement, Control, and Microtechnology existing interval tools have been extended and new modules have been developed. In this contribution, successful applications of interval algorithms to real-world problems in various fields of engineering are presented. The focus is on measuring techniques including interval observers and sensitivity analysis as well as design of optimal and robust controllers for continuous-time and discrete-time systems.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"436 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132471836","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}
Compensated algorithms improve the accuracy of a result evaluating a correcting term that compensates the finite precision of the computation. The implementation core of compensated algorithms is the computation of the rounding errors generated by the floating point operators. We focus this operator dependency discussing how to manage and to benefit from floating point arithmetic implemented through a fused multiply and add operator. We consider the compensation of dot product and polynomial evaluation with Horner iteration. In each case we provide theoretical a priori error bounds and numerical experiments to exhibit the best algorithmic choices with respect to accuracy or performance issues.
{"title":"Operator Dependant Compensated Algorithms","authors":"Philippe Langlois, N. Louvet","doi":"10.1109/SCAN.2006.36","DOIUrl":"https://doi.org/10.1109/SCAN.2006.36","url":null,"abstract":"Compensated algorithms improve the accuracy of a result evaluating a correcting term that compensates the finite precision of the computation. The implementation core of compensated algorithms is the computation of the rounding errors generated by the floating point operators. We focus this operator dependency discussing how to manage and to benefit from floating point arithmetic implemented through a fused multiply and add operator. We consider the compensation of dot product and polynomial evaluation with Horner iteration. In each case we provide theoretical a priori error bounds and numerical experiments to exhibit the best algorithmic choices with respect to accuracy or performance issues.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122988717","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}
Pub Date : 2006-07-10DOI: 10.1109/HPDC.2006.1652171
A. Frommer, Matthias Hüsken
Certain numerically intensive applications executed within a grid computing environment crucially depend on the properties of floating-point arithmetic implemented on the respective platform. Differences in these properties may have drastic effects. This paper identifies the central problems related to this situation. We propose an approach which gives the user valuable information on the various platforms available in a grid computing environment in order to assess the numerical quality of an algorithm run on each of these platforms. In this manner, the user will at least have very strong hints whether a program will perform reliably in a grid before actually executing it. Our approach extends the existing IeeeCC754 test suite by two "grid-enabled" modes: The first mode calculates a "numerical checksum" on a specific grid host and executes the job only if the checksum is identical to a locally generated one. The second mode provides the user with information on the reliability and IEEE 754-conformity of the underlying floating-point implementation of various platforms. Furthermore, it can help to find a set of compiler options to optimize the application's performance while retaining numerical stability.
{"title":"Ensuring Numerical Quality in Grid Computing","authors":"A. Frommer, Matthias Hüsken","doi":"10.1109/HPDC.2006.1652171","DOIUrl":"https://doi.org/10.1109/HPDC.2006.1652171","url":null,"abstract":"Certain numerically intensive applications executed within a grid computing environment crucially depend on the properties of floating-point arithmetic implemented on the respective platform. Differences in these properties may have drastic effects. This paper identifies the central problems related to this situation. We propose an approach which gives the user valuable information on the various platforms available in a grid computing environment in order to assess the numerical quality of an algorithm run on each of these platforms. In this manner, the user will at least have very strong hints whether a program will perform reliably in a grid before actually executing it. Our approach extends the existing IeeeCC754 test suite by two \"grid-enabled\" modes: The first mode calculates a \"numerical checksum\" on a specific grid host and executes the job only if the checksum is identical to a locally generated one. The second mode provides the user with information on the reliability and IEEE 754-conformity of the underlying floating-point implementation of various platforms. Furthermore, it can help to find a set of compiler options to optimize the application's performance while retaining numerical stability.","PeriodicalId":388600,"journal":{"name":"12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124397359","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：