Overdetermined
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Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares
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Author : Charles O. Stearns
language : en
Publisher:
Release Date : 1970
Convergence Of Iterative Methods Applied To Large Overdetermined Linear And Nonlinear Systems Of Equations Using Least Squares written by Charles O. Stearns and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Chebyshev polynomials categories.
Solutions are obtained to large overdetermined systems of equations. Both nonlinear and linear systems are considered. The nonlinear system represents a dipole model of the earth's geomagnetic field, which is generated from spherical harmonic coefficients. This system of 64 unknowns and 1836 equations is solved by a maximum neighborhood method, which is an optimum interpolation between the well known Taylor's series and steepest descent methods. The original given values of the generated field are as large as 60,000 gamma, whereas a rms residual of 27.9 gamma is obtained with 173 iterations. The linear system of equations represents dipole changes required to account for the earth's secular change field which is generated from spherical harmonic coefficients. The dipole parameters computed from the nonlinear model are used as input parameters. The system contains 64 unknowns and 612 equations and is solved using a Chebyshev polynomial iterative method. These results are compared to results obtained by a direct solution of the normal equations of the system and results obtained by a pseudo-inverse method using a modified Gram-Schmidt factorization. Although the latter two methods give smaller rms values than the iterative method, the results of the iterative method are more reasonable in view of known properties of the results. The generated field has a rms value of 45 gamma per year. An rms residual of 2.5 gamma per year was obtained after 25,000 iterations.
Algorithms For Solving Overdetermined Systems Of Linear Equations In The L P Subsript Sense
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Author : Robert William Owens
language : en
Publisher:
Release Date : 1975
Algorithms For Solving Overdetermined Systems Of Linear Equations In The L P Subsript Sense written by Robert William Owens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Algebras, Linear categories.
Kantian Ethics Almost Without Apology
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Author : Marcia W. Baron
language : en
Publisher: Cornell University Press
Release Date : 2018-10-18
Kantian Ethics Almost Without Apology written by Marcia W. Baron and has been published by Cornell University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-18 with Philosophy categories.
A reappraisal on the emphasis on duty in Immanuel Kant's ethics is long overdue. Marcia W. Baron evaluates and for the most part defends Kantian ethics against two frequent criticisms: that duty plays too large a role, leaving no room for the supererogatory; and that Kant places too much value on acting from duty. The author first argues that Kant's distinction between perfect and imperfect duties provides a plausible and intriguing alternative to contemporary approaches to charity, self-sacrifice, heroism, and saintliness. She probes the differences between the supererogationist and the Kantian, exploring the motivation between the former's position and bringing to light sharply divided views on the nature of moral constraint and excellence. Baron then confronts problems associated with Kant's account of moral motivation, she argues that the value that Kant attaches to acting from duty attaches primarily to governing ones conduct by a commitment to doing what morality asks. Thus understood, Kant's ethics steers clear of the most serious criticism. Of special interest is her discussion of overdetermination. Clearly written and cogently argued, Kantian Ethics Almost without Apology takes on the most philosophically intriguing challenges to Kantian ethics and subjects them to a rigorous yet sympathetic assessment. Readers will find here original contributions to the debate over impartial morality.
Principles Of Object Oriented Modeling And Simulation With Modelica 2 1
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Author : Peter Fritzson
language : en
Publisher: John Wiley & Sons
Release Date : 2010-08-31
Principles Of Object Oriented Modeling And Simulation With Modelica 2 1 written by Peter Fritzson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-31 with Computers categories.
Provides an introduction to modern object-oriented design principles and applications for the fast-growing area of modeling and simulation Covers the topic of multi-domain system modeling and design with applications that have components from several areas Serves as a reference for the Modelica language as well as a comprehensive overview of application model libraries for a number of application domains
Star Adaptation Of Qr Algorithm For Overdetermined Linear Systems With Complex Coefficients
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Author :
language : en
Publisher:
Release Date : 1981
Star Adaptation Of Qr Algorithm For Overdetermined Linear Systems With Complex Coefficients written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Elementary Linear Algebra
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Author : Howard Anton
language : en
Publisher: John Wiley & Sons
Release Date : 2010-03-15
Elementary Linear Algebra written by Howard Anton and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-15 with Mathematics categories.
When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.
Distribution Of Error In Least Squares Solution Of An Overdetermined System Of Linear Simultaneous Equations
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Author : C. David Miller
language : en
Publisher:
Release Date : 1972
Distribution Of Error In Least Squares Solution Of An Overdetermined System Of Linear Simultaneous Equations written by C. David Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Equations, Simultaneous categories.
Probability density functions were derived for errors in the evaluation of unknowns by the least squares method in system of nonhomogeneous linear equations. Coefficients of the unknowns were assumed correct and computational precision were also assumed. A vector space was used, with number of dimensions equal to the number of equations. An error vector was defined and assumed to have uniform distribution of orientation throughout the vector space. The density functions are shown to be insensitive to the biasing effects of the source of the system of equations.
Explaining Emotions
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Author : Amélie Rorty
language : en
Publisher: Univ of California Press
Release Date : 1980-05-09
Explaining Emotions written by Amélie Rorty and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-05-09 with Philosophy categories.
The challenge of explaining the emotions has engaged the attention of the best minds in philosophy and science throughout history. Part of the fascination has been that the emotions resist classification. As adequate account therefore requires receptivity to knowledge from a variety of sources. The philosopher must inform himself of the relevant empirical investigation to arrive at a definition, and the scientist cannot afford to be naive about the assumptions built into his conceptual apparatus. The contributors to this volume have approached the problem of characterizing and classifying emotions from the perspectives of neurophysiology, psychology, and social psychology as well as that of philosophical psychology. They discuss the difficulties that arise in classifying the emotions, assessing their appropriateness and rationality, and determining their function in motivating moral action.
Mathematical Geosciences
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Author : Joseph L. Awange
language : en
Publisher: Springer Nature
Release Date : 2023-04-07
Mathematical Geosciences written by Joseph L. Awange and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Science categories.
This second edition of Mathematical Geosciences book adds five new topics: Solution equations with uncertainty, which proposes two novel methods for solving nonlinear geodetic equations as stochastic variables when the parameters of these equations have uncertainty characterized by probability distribution. The first method, an algebraic technique, partly employs symbolic computations and is applicable to polynomial systems having different uncertainty distributions of the parameters. The second method, a numerical technique, uses stochastic differential equation in Ito form; Nature Inspired Global Optimization where Meta-heuristic algorithms are based on natural phenomenon such as Particle Swarm Optimization. This approach simulates, e.g., schools of fish or flocks of birds, and is extended through discussion of geodetic applications. Black Hole Algorithm, which is based on the black hole phenomena is added and a new variant of the algorithm code is introduced and illustrated based on examples; The application of the Gröbner Basis to integer programming based on numeric symbolic computation is introduced and illustrated by solving some standard problems; An extension of the applications of integer programming solving phase ambiguity in Global Navigation Satellite Systems (GNSSs) is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. Three alternative algorithms are suggested, two of which are based on local and global linearization via McCormic Envelopes; and Machine learning techniques (MLT) that offer effective tools for stochastic process modelling. The Stochastic Modelling section is extended by the stochastic modelling via MLT and their effectiveness is compared with that of the modelling via stochastic differential equations (SDE). Mixing MLT with SDE also known as frequently Neural Differential Equations is also introduced and illustrated by an image classification via a regression problem.
Electromagnetic Modeling Of Composite Metallic And Dielectric Structures
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Author : Branko M. Kolundžija
language : en
Publisher: Artech House
Release Date : 2002
Electromagnetic Modeling Of Composite Metallic And Dielectric Structures written by Branko M. Kolundžija and has been published by Artech House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
This practical new resource provides you with a much wider choice of analytical solutions to the everyday problems you encounter in electromagnetic modeling. The book enables you to use cutting-edge method-of-moments procedures, with new theories and techniques that help you optimize computer performance in numerical analysis of composite metallic and dielectric structures in the complex frequency domain.