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Guaranteed Estimation Problems In The Theory Of Linear Ordinary Differential Equations With Uncertain Data
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Book Synopsis Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data by : Oleksandr Nakonechnyi
Download or read book Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data written by Oleksandr Nakonechnyi and published by CRC Press. This book was released on 2022-09-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.
Book Synopsis System Analysis & Intelligent Computing by : Michael Zgurovsky
Download or read book System Analysis & Intelligent Computing written by Michael Zgurovsky and published by Springer Nature. This book was released on 2022-03-25 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains the newest advances related to research and development of complex intellectual systems of various nature, acting under conditions of uncertainty and multifactor risks, intelligent systems for decision-making, high performance computing, state-of-the-art information technologies for needs of science, industry, economy, and environment. The most important problems of sustainable development and global threats estimation, forecast and foresight in tasks of planning and strategic decision-making are investigated. This monograph will be useful to researchers, post-graduates, and advanced students specializing in system analysis, decision-making, strategic planning or engineering design, fundamentals of computational Intelligence, artificial Intelligence systems based on hybrid neural networks, big data, and data mining.
Book Synopsis Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data by : Oleksandr Nakonechnyi
Download or read book Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data written by Oleksandr Nakonechnyi and published by . This book was released on 2024-10-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.
Book Synopsis Inverse Problems and Large-Scale Computations by : Larisa Beilina
Download or read book Inverse Problems and Large-Scale Computations written by Larisa Beilina and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of two international workshops, namely the Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, held jointly in Sunne, Sweden from May 1-6 2012. The subject of the inverse problems workshop was to present new analytical developments and new numerical methods for solutions of inverse problems. The objective of the large-scale modeling workshop was to identify large-scale problems arising in various fields of science and technology and covering all possible applications, with a particular focus on urgent problems in theoretical and applied electromagnetics. The workshops brought together scholars, professionals, mathematicians, and programmers and specialists working in large-scale modeling problems. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.
Book Synopsis Foundations of Theoretical Approaches in Systems Biology by : Alberto Marin-Sanguino
Download or read book Foundations of Theoretical Approaches in Systems Biology written by Alberto Marin-Sanguino and published by Frontiers Media SA. This book was released on 2019-01-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: If biology in the 20th century was characterized by an explosion of new technologies and experimental methods, that of the 21st has seen an equally exuberant proliferation of mathematical and computational methods that attempt to systematize and explain the abundance of available data. As we live through the consolidation of a new paradigm where experimental data goes hand in hand with computational analysis, we contemplate the challenge of fusing these two aspects of the new biology into a consistent theoretical framework. Whether systems biology will survive as a field or be washed away by the tides of future fads will ultimately depend on its success to achieve this type of synthesis. The famous quote attributed to Kurt Lewin comes to mind: "there is nothing more practical than a good theory". This book presents a wide assortment of articles on systems biology in an attempt to capture the variety of current methods in systems biology and show how they can help to find answers to the challenges of modern biology.
Book Synopsis Algebraic Statistics by : Seth Sullivant
Download or read book Algebraic Statistics written by Seth Sullivant and published by American Mathematical Soc.. This book was released on 2018-11-19 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Book Synopsis Attractive Ellipsoids in Robust Control by : Alexander Poznyak
Download or read book Attractive Ellipsoids in Robust Control written by Alexander Poznyak and published by Springer. This book was released on 2014-09-29 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the “attractive ellipsoid method.” Along with a coherent introduction to the proposed control design and related topics, the monograph studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties. The authors discuss linear-style feedback control synthesis in the context of the above-mentioned systems. The development and physical implementation of high-performance robust-feedback controllers that work in the absence of complete information is addressed, with numerous examples to illustrate how to apply the attractive ellipsoid method to mechanical and electromechanical systems. While theorems are proved systematically, the emphasis is on understanding and applying the theory to real-world situations. Attractive Ellipsoids in Robust Control will appeal to undergraduate and graduate students with a background in modern systems theory as well as researchers in the fields of control engineering and applied mathematics.
Book Synopsis Principles of Integrated Airborne Avionics by : Igor Victorovich Avtin
Download or read book Principles of Integrated Airborne Avionics written by Igor Victorovich Avtin and published by Springer Nature. This book was released on 2021-06-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the principles, approaches, concepts and development programs for integrated aircraft avionics. The functional tasks of integrated on-board radio electronic equipment (avionics) of navigation, landing, data exchange and air traffic control are formulated that meet the modern requirements of civil and military aviation, and the principles of avionics integration are proposed. The modern approaches to the joint processing of information in navigation and landing complexes are analyzed. Algorithms of multichannel information processing in integrated avionics are considered, and examples of its implementation are presented. This book is intended for scientists and professionals in the field of aviation equipment, students and graduate students of relevant specialties.
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations by : Donald J. Estep
Download or read book Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations written by Donald J. Estep and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Book Synopsis Discrete Inverse and State Estimation Problems by : Carl Wunsch
Download or read book Discrete Inverse and State Estimation Problems written by Carl Wunsch and published by Cambridge University Press. This book was released on 2006-06-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing the problems of making inferences from noisy observations and imperfect theories, this 2006 book introduces many inference tools and practical applications. Starting with fundamental algebraic and statistical ideas, it is ideal for graduate students and researchers in oceanography, climate science, and geophysical fluid dynamics.
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Book Synopsis International Aerospace Abstracts by :
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1997 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Ordinary Differential Equations by : Earl A. Coddington
Download or read book Theory of Ordinary Differential Equations written by Earl A. Coddington and published by Krieger Publishing Company. This book was released on 1955 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable. It has been developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician.
