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ISBN: 3110498057 3110499460 9783110499469 9783110498059 3110500639 Year: 2017 Publisher: Berlin/Boston De Gruyter
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This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals
Interval analysis (Mathematics) --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Numerical analysis
Book
ISBN: 1536120499 9781536120493 9781536120288 Year: 2017 Publisher: Hauppauge, New York
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Interval analysis (Mathematics) --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Numerical analysis
Book
ISBN: 1000097527 3731509652 Year: 2022 Publisher: Karlsruhe KIT Scientific Publishing
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This work introduces a new specification and verification approach for dynamic systems. The introduced approach is able to provide type II error free results by definition, i.e. there are no hidden faults in the verification result. The approach is based on Kaucher interval arithmetic to enclose the measurement in a bounded error sense. The developed methods are proven mathematically to provide a reliable verification for a wide class of safety critical systems.
Electrical engineering --- Verifikation --- Dynamische Systeme --- Intervall Arithmetik --- Diagnose --- Bounded Error --- Verification --- Dynamic Systems --- Interval Arithmetic --- Diagnosis
ISBN: 1139886223 1107102537 0511943970 0521102146 1107087783 0511526474 1107094038 110709089X 9781107087781 9780511526473 052133196X 9780521331968 9781139886222 9781107102538 9780511943973 9780521102148 9781107094031 Year: 1990 Publisher: Cambridge [England] ; New York : Cambridge University Press,
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An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigour. In order to keep the book self-contained, various results from linear algebra (Perron-Frobenius theory, M- and H- matrices) and analysis (existence of solutions to nonlinear systems) are proved, often from a novel and more general viewpoint. An extensive bibliography is included.
Interval analysis (Mathematics) --- Equations --- Algebra --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Numerical analysis --- Numerical solutions. --- Graphic methods
ISBN: 3527401342 Year: 1998 Publisher: Berlin Wiley
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Programming --- Interval analysis (Mathematics) --- 519.6 --- 681.3 *G10 --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Numerical analysis --- Computational mathematics. Numerical analysis. Computer programming --- Computerwetenschap--?*G10 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Calcul numerique --- Approximation dans le domaine complexe --- Calcul d'erreur
ISBN: 0125188501 1322478066 1483273849 9780125188500 Year: 1980 Publisher: New York (N.Y.): Academic press,
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Numerical analysis --- Interval analysis (Mathematics) --- Congresses --- -519.6 --- 681.3 *G10 --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Computational mathematics. Numerical analysis. Computer programming --- Computerwetenschap--?*G10 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Interval analysis (Mathematics) - Congresses
ISBN: 0120498200 0080916368 1299224318 9780120498208 Year: 1983 Publisher: New York (N.Y.): Academic press,
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Programming --- Numerical analysis --- Interval analysis (Mathematics) --- 519.6 --- 681.3*G1 --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Computational mathematics. Numerical analysis. Computer programming --- 681.3*G1 Numerical analysis --- 519.6 Computational mathematics. Numerical analysis. Computer programming
ISBN: 0898711614 9780898711615 Year: 1979 Volume: 2 Publisher: Philadelphia (Pa.): Society for industrial and applied mathematics,
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Numerical analysis --- Interval analysis (Mathematics) --- #KVIV --- 519.6 --- 681.3*G1 --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Computational mathematics. Numerical analysis. Computer programming --- Interval analysis (Mathematics). --- 681.3*G1 Numerical analysis --- 519.6 Computational mathematics. Numerical analysis. Computer programming
ISBN: 1280243430 9786610243433 1423799240 160750121X 6000003765 1601291027 9781423799245 9781601291028 9781607501213 9781586035327 1586035320 Year: 2005 Publisher: Amsterdam Washington, D.C. IOS Press
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Focuses on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the formalism of Constraint Satisfaction Differential Problems. Such a framework allows the specification of ordinary differential equations by means of constraints.
Constraints (Artificial intelligence) --- Differential equations. --- Interval analysis (Mathematics) --- Biophysics --- Biological physics --- Biology --- Medical sciences --- Physics --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Numerical analysis --- 517.91 Differential equations --- Differential equations --- Constraint satisfaction (Artificial intelligence) --- Artificial intelligence --- Mathematical models. --- Mathematical models --- E-books
Book
ISBN: 0824786963 Year: 1992 Volume: vol 165 Publisher: New York (N.Y.) : Dekker,
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Mathematical control systems --- Calcul sur des intervalles --- Interval analyse (Wiskunde) --- Interval analysis (Mathematics) --- Mathematical optimization --- Niet-lineaire programmering --- Nonlinear programming --- Optimalisation mathématique --- Programmation non lineaire --- Wiskundige optimisatie --- Optimisation mathématique --- Programmation non linéaire --- Programming (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Analysis, Interval --- Arithmetic, Interval --- Interval arithmetic --- Interval mathematics --- Mathematics, Interval --- Mathematics --- Numerical analysis --- Mathematical optimization. --- Nonlinear programming. --- Interval analysis (Mathematics). --- Optimisation mathématique --- Programmation non linéaire
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