Book•
Applied Interval Analysis
30 Aug 2001-
About: The article was published on 2001-08-30 and is currently open access. It has received 1709 citations till now. The article focuses on the topics: Interval arithmetic.
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02 Jan 2016
TL;DR: In this paper, the authors present an ALGOLGOL-based approach for the inclusion of complex Zeros of polynomials of a function of one real variable in a system of linear systems of equations.
Abstract: Preface to the English Edition. Preface to the German Edition. Real Interval Arithmetic. Further Concepts and Properties. Interval Evaluation and Range of Real Functions. Machine Interval Arithmetic. Complex Interval Arithmetic. Metric, Absolute, Value, and Width in. Inclusion of Zeros of a Function of One Real Variable. Methods for the Simultaneous Inclusion of Real Zeros of Polynomials. Methods for the Simultaneous Inclusion of Complex Zeros of Polynomials. Interval Matrix Operations. Fixed Point Iteration for Nonlinear Systems of Equations. Systems of Linear Equations Amenable to Interation. Optimality of the Symmetric Single Step Method with Taking Intersection after Every Component. On the Feasibility of the Gaussian Algorithm for Systems of Equations with Intervals as Coefficients. Hansen's Method. The Procedure of Kupermann and Hansen. Ireation Methods for the Inclusion of the Inverse Matrix and for Triangular Decompositions. Newton-like Methods for Nonlinear Systems of Equations. Newton-like Methods without Matrix Inversions. Newton-like Methods for Particular Systems of Nonlinear Equations. Newton-like Total step and Single Step Methods. Appendix A. The Order of Convergence of Iteration Methods in vn(Ic) and Mmn(iC) ). Appendix B. Realizations of Machine Interval Arithmetics in ALGOL 60. Appendix C. ALGOL Procedures. Bibliography. Index of Notation. Subject Index.
2,054 citations
TL;DR: Sampling-based methods for uncertainty and sensitivity analysis are reviewed and special attention is given to the determination of sensitivity analysis results.
1,179 citations
Cites background from "Applied Interval Analysis"
...Alternative representations for uncertainty such as evidence theory and possibility theory merit consideration for their potential to represent uncertainty in situations where little information is available [84–92]....
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..., evidence theory, possibility theory, fuzzy set theory, interval analysis) are active areas of research [84–92] but are outside the intended scope of this presentation....
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Book•
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24 Jun 2003
TL;DR: Digital Arithmetic, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner, to develop sound solutions, avoid known mistakes, and repeat successful design decisions.
Abstract: Digital arithmetic plays an important role in the design of general-purpose digital processors and of embedded systems for signal processing, graphics, and communications. In spite of a mature body of knowledge in digital arithmetic, each new generation of processors or digital systems creates new arithmetic design problems. Designers, researchers, and graduate students will find solid solutions to these problems in this comprehensive, state-of-the-art exposition of digital arithmetic. Ercegovac and Lang, two of the field's leading experts, deliver a unified treatment of digital arithmetic, tying underlying theory to design practice in a technology-independent manner. They consistently use an algorithmic approach in defining arithmetic operations, illustrate concepts with examples of designs at the logic level, and discuss cost/performance characteristics throughout. Students and practicing designers alike will find Digital Arithmetic a definitive reference and a consistent teaching tool for developing a deep understanding of the "arithmetic style" of algorithms and designs. Guides readers to develop sound solutions, avoid known mistakes, and repeat successful design decisions. Presents comprehensive coveragefrom fundamental theories to current research trends. Written in a clear and engaging style by two masters of the field. Concludes each chapter with in-depth discussions of the key literature. Includes a full set of over 250 exercises, an on-line appendix with solutions to one-third of the exercises and 600 lecture slides
742 citations
TL;DR: This article reviews identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiable analysis, practical identIFiability analysis and sensitivity-based identifability analysis.
Abstract: Ordinary differential equations (ODEs) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last two decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determining unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past couple of decades, including structural identifiability analysis, practical identifiability analysis, and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV and influenza viruses are given to illustrate how to apply these identifiability analysis methods in practice.
506 citations
Cites methods from "Applied Interval Analysis"
...For details of the algorithms for solving CSPs (called interval arithmetic), see [53]....
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TL;DR: This survey covers the state of the art of techniques for solving general-purpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques that provably find all solutions (if there are finitely many).
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461 citations
Cites background from "Applied Interval Analysis"
...5:21–22)...
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...Many more applications can be found in the books by Pintér (1996a), Floudas and Pardalos (1990), Floudas et al. (1999) and Jaulin et al. (2001)....
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References
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Book•
01 Aug 1989TL;DR: The design and analysis of spatial data structures and applications for predicting stock returns and remembering and imagining palestine identity and service manual are studied.
Abstract: the design and analysis of spatial data structures addison the design and analysis of spatial data structures addison the design and analysis of spatial data structures addison the design and analysis of spatial data structures addison the design and analysis of spatial data structures addison applications of spatial data structures: computer graphics the design and analysis of spatial data structures (pdf editor: andrew s. glassner computer foundations of mathematics 10 by addison wesley bing the value of social media for predicting stock returns landscape architecture fourth edition a manual of land portland writing units grade 5 ekpbs samsung odin manual pdf pdf duckshost wheres the bee wire o journal wmcir document about oae special education 043 secrets study chapter 15 section 2 guided reading a worldwide depression private lemonade nfcqr songs made famous by tammy wynette mandv chapter 22 the great depression begins test answers shamrock cargo a story of the irish pota ekpbs tlia2050a learner guide ramonapropertymanagers 12. greene n., kass m., miller g. “hierarchical zbuffer the encyclopedia of the novel vmnlaw remembering and imagining palestine identity and service manual tc21da jupw websters new world basic dictionary of american english workshop manual for mercedes benz oligra
2,783 citations
"Applied Interval Analysis" refers background in this paper
...Regular subpavings (Jaulin, 1994; Sam-Haroud and Faltings, 1996), also called n-trees (Samet, 1990), are a class of subsets of lRn easily manipulated with a computer as we shall see....
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TL;DR: A collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects that transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object.
Abstract: This paper describes a collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects. The algorithm transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object. A trajectory of this reference point which avoids all forbidden regions is free of collisions. Trajectories are found by searching a network which indicates, for each vertex in the transformed obstacles, which other vertices can be reached safely.
2,396 citations
"Applied Interval Analysis" refers methods in this paper
...of the methods available in the literature are based on the concept of configuration space (or C-space) (Lozano-Perez and Wesley, 1979)....
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01 Jun 1965
TL;DR: In this article, the authors describe a six-degree-of-freedom control with six motors, each having a ground abutment, for simulating flight conditions in the training of pilots.
Abstract: This paper describes a mechanism which has six degrees of freedom, controlled in any combination by six motors, each having a ground abutment. It is considered that by its particular arrangement, this mechanism may form an elegant design for simulating flight conditions in the training of pilots. Unlike most simulators, it has no fixed axes relative to the ground, and therefore within the limits of amplitude of the design it can truly simulate the conditions of banking by carrying the simulation of control surfaces into the axes of the new attitude.Variations in control arrangements are described and their respective design merits considered.Other possible uses for this mechanism are mentioned, including automation of production.
2,341 citations
01 Oct 1992
TL;DR: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented.
Abstract: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented. Complete information about a freespace and goal is encoded in the form of a special artificial potential function, called a navigation function, that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. A formula for navigation functions that guide a point-mass robot in a generalized sphere world is developed. The simplest member of this family is a space obtained by puncturing a disk by an arbitrary number of smaller disjoint disks representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation. Simulation results for planar scenarios are provided. >
1,912 citations
"Applied Interval Analysis" refers background in this paper
...This problem of path planning in a known environment has received considerable attention (Nilsson, 1969; LozanoPerez, 1981; O'Dunlaing and Yap, 1982; Rimon and Koditschek, 1992)....
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01 Jun 1991
TL;DR: An algorithm for, model-based localization that relies on the concept of a geometric beacon, a naturally occurring environment feature that can be reliably observed in successive sensor measurements and can be accurately described in terms of a concise geometric parameterization, is developed.
Abstract: The application of the extended Kaman filter to the problem of mobile robot navigation in a known environment is presented. An algorithm for, model-based localization that relies on the concept of a geometric beacon, a naturally occurring environment feature that can be reliably observed in successive sensor measurements and can be accurately described in terms of a concise geometric parameterization, is developed. The algorithm is based on an extended Kalman filter that utilizes matches between observed geometric beacons and an a priori map of beacon locations. Two implementations of this navigation algorithm, both of which use sonar, are described. The first implementation uses a simple vehicle with point kinematics equipped with a single rotating sonar. The second implementation uses a 'Robuter' mobile robot and six static sonar transducers to provide localization information while the vehicle moves at typical speeds of 30 cm/s. >
1,394 citations
"Applied Interval Analysis" refers methods in this paper
...Indeed, once a reasonably accurate initialization has been performed, it is often possible to use a well established local tracking technique such as extended Kalman filtering (Leonard and Durrant-Whyte, 1991) or its bounded-error counterpart (Hanebeck and Schmidt, 1996; Meizel et al....
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