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Discrete Polynomial Spline Approximation Methods
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Book Synopsis Methods of Shape-preserving Spline Approximation by : Boris I. Kvasov
Download or read book Methods of Shape-preserving Spline Approximation written by Boris I. Kvasov and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
Book Synopsis Approximation and Modeling with B-Splines by : Klaus Hollig
Download or read book Approximation and Modeling with B-Splines written by Klaus Hollig and published by SIAM. This book was released on 2015-07-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Progress on Difference Equations and Discrete Dynamical Systems by : Steve Baigent
Download or read book Progress on Difference Equations and Discrete Dynamical Systems written by Steve Baigent and published by Springer Nature. This book was released on 2021-01-04 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability. Other chapters cover the latest personal research contributions of the author(s) in their particular area of expertise and range from the more technical articles on abstract systems to those that discuss the application of difference equations to real-world problems. The book is of interest to both Ph.D. students and researchers alike who wish to keep abreast of the latest developments in difference equations and discrete dynamical systems.
Book Synopsis Handbook of Splines by : Gheorghe Micula
Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Methods in Computer Aided Geometric Design II by : Tom Lyche
Download or read book Mathematical Methods in Computer Aided Geometric Design II written by Tom Lyche and published by Academic Press. This book was released on 2014-05-10 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Methods in Computer Aided Geometric Design II covers the proceedings of the 1991 International Conference on Curves, Surfaces, CAGD, and Image Processing, held at Biri, Norway. This book contains 48 chapters that include the topics of blossoming, cyclides, data fitting and interpolation, and finding intersections of curves and surfaces. Considerable chapters explore the geometric continuity, geometrical optics, image and signal processing, and modeling of geological structures. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.
Download or read book Spline Functions written by K. Böhmer and published by Springer. This book was released on 2006-11-14 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spline and Spline Wavelet Methods with Applications to Signal and Image Processing by : Amir Z. Averbuch
Download or read book Spline and Spline Wavelet Methods with Applications to Signal and Image Processing written by Amir Z. Averbuch and published by Springer Science & Business Media. This book was released on 2014-04-08 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images up sampling. In addition to the design of a diverse library of splines, SW, SWP and SWF, this book describes their applications to practical problems. The applications include up sampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SWF are utilized for image restoration that was degraded by noise, blurring and loss of significant number of pixels. The book is accompanied by Matlab based software that demonstrates and implements all the presented algorithms. The book combines extensive theoretical exposure with detailed description of algorithms, applications and software. The Matlab software can be downloaded from http://extras.springer.com
Book Synopsis Bézier and Splines in Image Processing and Machine Vision by : Sambhunath Biswas
Download or read book Bézier and Splines in Image Processing and Machine Vision written by Sambhunath Biswas and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with various image processing and machine vision problems efficiently with splines and includes: the significance of Bernstein Polynomial in splines, detailed coverage of Beta-splines applications which are relatively new, Splines in motion tracking, various deformative models and their uses. Finally the book covers wavelet splines which are efficient and effective in different image applications.
Book Synopsis Computation of Curves and Surfaces by : Wolfgang Dahmen
Download or read book Computation of Curves and Surfaces written by Wolfgang Dahmen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assembled here is a collection of articles presented at a NATO ADVANCED STU DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.
Book Synopsis Recent Progress in Inequalities by : G.V. Milovanovic
Download or read book Recent Progress in Inequalities written by G.V. Milovanovic and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.
Book Synopsis Approximation Theory and Approximation Practice, Extended Edition by : Lloyd N. Trefethen
Download or read book Approximation Theory and Approximation Practice, Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Information-Theoretic Methods for Estimating of Complicated Probability Distributions by : Zhi Zong
Download or read book Information-Theoretic Methods for Estimating of Complicated Probability Distributions written by Zhi Zong and published by Elsevier. This book was released on 2006-08-15 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC- density functions automatically determined from samples- Free of assuming density forms- Computation-effective methods suitable for PC
Book Synopsis Numerical Methods for Engineers and Scientists, Second Edition, by : Joe D. Hoffman
Download or read book Numerical Methods for Engineers and Scientists, Second Edition, written by Joe D. Hoffman and published by CRC Press. This book was released on 2001-05-31 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."
Book Synopsis Numerical Approximation Methods by : Harold Cohen
Download or read book Numerical Approximation Methods written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2011-09-28 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Book Synopsis Approximation Theory and Methods by : M. J. D. Powell
Download or read book Approximation Theory and Methods written by M. J. D. Powell and published by Cambridge University Press. This book was released on 1981-03-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Book Synopsis Frontiers in Applied General Equilibrium Modeling by : Timothy J. Kehoe
Download or read book Frontiers in Applied General Equilibrium Modeling written by Timothy J. Kehoe and published by Cambridge University Press. This book was released on 2005-01-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 volume brings together twelve papers by many of the most prominent applied general equilibrium modelers honoring Herbert Scarf, the father of equilibrium computation in economics. It deals with developments in applied general equilibrium, a field which has broadened greatly since the 1980s. The contributors discuss some traditional as well as some modern topics in the field, including non-convexities in economy-wide models, tax policy, developmental modeling and energy modeling. The book also covers a range of distinct approaches, conceptual issues and computational algorithms, such as calibration and areas of application such as macroeconomics of real business cycles and finance. An introductory chapter written by the editors maps out issues and scenarios for the future evolution of applied general equilibrium.
