Multivariate Splines

Multivariate Splines
Author: Charles K. Chui
Publisher: SIAM
Total Pages: 192
Release: 1988-01-01
Genre: Mathematics
ISBN: 0898712262

Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Advances in Aerospace Guidance, Navigation and Control

Advances in Aerospace Guidance, Navigation and Control
Author: Qiping Chu
Publisher: Springer Science & Business Media
Total Pages: 773
Release: 2013-11-18
Genre: Technology & Engineering
ISBN: 3642382533

Following the successful 1st CEAS (Council of European Aerospace Societies) Specialist Conference on Guidance, Navigation and Control (CEAS EuroGNC) held in Munich, Germany in 2011, Delft University of Technology happily accepted the invitation of organizing the 2nd CEAS EuroGNC in Delft, The Netherlands in 2013. The goal of the conference is to promote new advances in aerospace GNC theory and technologies for enhancing safety, survivability, efficiency, performance, autonomy and intelligence of aerospace systems using on-board sensing, computing and systems. A great push for new developments in GNC are the ever higher safety and sustainability requirements in aviation. Impressive progress was made in new research fields such as sensor and actuator fault detection and diagnosis, reconfigurable and fault tolerant flight control, online safe flight envelop prediction and protection, online global aerodynamic model identification, online global optimization and flight upset recovery. All of these challenges depend on new online solutions from on-board computing systems. Scientists and engineers in GNC have been developing model based, sensor based as well as knowledge based approaches aiming for highly robust, adaptive, nonlinear, intelligent and autonomous GNC systems. Although the papers presented at the conference and selected in this book could not possibly cover all of the present challenges in the GNC field, many of them have indeed been addressed and a wealth of new ideas, solutions and results were proposed and presented. For the 2nd CEAS Specialist Conference on Guidance, Navigation and Control the International Program Committee conducted a formal review process. Each paper was reviewed in compliance with good journal practice by at least two independent and anonymous reviewers. The papers published in this book were selected from the conference proceedings based on the results and recommendations from the reviewers.

Multiple Model Approaches To Nonlinear Modelling And Control

Multiple Model Approaches To Nonlinear Modelling And Control
Author: R Murray-Smith
Publisher: CRC Press
Total Pages: 361
Release: 2020-11-25
Genre: Technology & Engineering
ISBN: 100012407X

This work presents approaches to modelling and control problems arising from conditions of ever increasing nonlinearity and complexity. It prescribes an approach that covers a wide range of methods being combined to provide multiple model solutions. Many component methods are described, as well as discussion of the strategies available for building a successful multiple model approach.

Handbook of Splines

Handbook of Splines
Author: Gheorghe Micula
Publisher: Springer Science & Business Media
Total Pages: 622
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401153388

The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.

Multivariate Polysplines

Multivariate Polysplines
Author: Ognyan Kounchev
Publisher: Academic Press
Total Pages: 513
Release: 2001-06-11
Genre: Mathematics
ISBN: 0080525008

Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. - Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic - Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines - Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case - Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property

Spline Models for Observational Data

Spline Models for Observational Data
Author: Grace Wahba
Publisher: SIAM
Total Pages: 174
Release: 1990-09-01
Genre: Mathematics
ISBN: 0898712440

This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.

Scientific and Technical Aerospace Reports

Scientific and Technical Aerospace Reports
Author:
Publisher:
Total Pages: 652
Release: 1995
Genre: Aeronautics
ISBN:

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Hybrid Systems: Computation and Control

Hybrid Systems: Computation and Control
Author: Joao Hespanha
Publisher: Springer Science & Business Media
Total Pages: 595
Release: 2006-03-20
Genre: Computers
ISBN: 3540331700

This book constitutes the refereed proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control, HSCC 2006, held in Santa Barbara, CA, USA in March 2006. The 39 revised full papers presented together with the abstracts of 3 invited talks were carefully reviewed and selected from 79 submissions. Among the topics addressed are tools for analysis and verification, control and optimization, modeling, engineering applications, and emerging directions in programming language support and implementation. The papers focus on modeling, analysis, and implementation of dynamic and reactive systems involving both discrete and continuous behaviors.

Approximation and Modeling with B-Splines

Approximation and Modeling with B-Splines
Author: Klaus Hollig
Publisher: SIAM
Total Pages: 228
Release: 2015-07-01
Genre: Mathematics
ISBN: 1611972949

B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Spline Models for Observational Data

Spline Models for Observational Data
Author: Grace Wahba
Publisher: SIAM
Total Pages: 181
Release: 1990-01-01
Genre: Mathematics
ISBN: 9781611970128

This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.