Interpolation And Approximation With Splines And Fractals

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Interpolation and Approximation with Splines and Fractals

Author : Peter Robert Massopust
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Interpolation and Approximation with Splines and Fractals by : Peter Robert Massopust

Download or read book Interpolation and Approximation with Splines and Fractals written by Peter Robert Massopust and published by . This book was released on 2010 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material.

Analysis, Probability And Mathematical Physics On Fractals

Author : Patricia Alonso Ruiz
Publisher : World Scientific
ISBN 13 : 9811215545
Total Pages : 594 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Analysis, Probability And Mathematical Physics On Fractals by : Patricia Alonso Ruiz

Download or read book Analysis, Probability And Mathematical Physics On Fractals written by Patricia Alonso Ruiz and published by World Scientific. This book was released on 2020-02-26 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.

Frontiers in Industrial and Applied Mathematics

Author : Rajesh Kumar Sharma
Publisher : Springer Nature
ISBN 13 : 9811972729
Total Pages : 659 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Frontiers in Industrial and Applied Mathematics by : Rajesh Kumar Sharma

Download or read book Frontiers in Industrial and Applied Mathematics written by Rajesh Kumar Sharma and published by Springer Nature. This book was released on 2023-02-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21–22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.

Fractal Geometry

Author : Kenneth Falconer
Publisher : John Wiley & Sons
ISBN 13 : 111994239X
Total Pages : 404 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Fractal Geometry by : Kenneth Falconer

Download or read book Fractal Geometry written by Kenneth Falconer and published by John Wiley & Sons. This book was released on 2014-02-03 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)

Spline Functions

Author : Larry L. Schumaker
Publisher : SIAM
ISBN 13 : 1611973902
Total Pages : 420 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Spline Functions by : Larry L. Schumaker

Download or read book Spline Functions written by Larry L. Schumaker and published by SIAM. This book was released on 2015-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.

Fractal Functions, Fractal Surfaces, and Wavelets

Author : Peter R. Massopust
Publisher : Academic Press
ISBN 13 : 0128044705
Total Pages : 428 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Fractal Functions, Fractal Surfaces, and Wavelets by : Peter R. Massopust

Download or read book Fractal Functions, Fractal Surfaces, and Wavelets written by Peter R. Massopust and published by Academic Press. This book was released on 2016-09-02 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust's work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content. - Offers a comprehensive presentation of fractal functions and fractal surfaces - Includes latest developments in fractal interpolation - Connects fractal geometry with wavelet theory - Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets - Deepens and extends the pedagogical content

Fractal Patterns in Nonlinear Dynamics and Applications

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1351647628
Total Pages : 148 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Fractal Patterns in Nonlinear Dynamics and Applications by : Santo Banerjee

Download or read book Fractal Patterns in Nonlinear Dynamics and Applications written by Santo Banerjee and published by CRC Press. This book was released on 2020-03-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.

Frontiers of Fractal Analysis

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1000625877
Total Pages : 183 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Frontiers of Fractal Analysis by : Santo Banerjee

Download or read book Frontiers of Fractal Analysis written by Santo Banerjee and published by CRC Press. This book was released on 2022-07-07 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Handbook of Splines

Author : Gheorghe Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401153388
Total Pages : 622 pages
Book Rating : 4.4/5 (11 download)

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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.

Applied Analysis, Optimization and Soft Computing

Author : Tanmoy Som
Publisher : Springer Nature
ISBN 13 : 9819905974
Total Pages : 425 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Applied Analysis, Optimization and Soft Computing by : Tanmoy Som

Download or read book Applied Analysis, Optimization and Soft Computing written by Tanmoy Som and published by Springer Nature. This book was released on 2023-06-10 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields.

Computational Methods for Numerical Analysis with R

Author : James P Howard, II
Publisher : CRC Press
ISBN 13 : 1351646508
Total Pages : 274 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Computational Methods for Numerical Analysis with R by : James P Howard, II

Download or read book Computational Methods for Numerical Analysis with R written by James P Howard, II and published by CRC Press. This book was released on 2017-07-12 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Operator Methods in Wavelets, Tilings, and Frames

Author : Keri A. Kornelson
Publisher : American Mathematical Soc.
ISBN 13 : 1470410400
Total Pages : 192 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Operator Methods in Wavelets, Tilings, and Frames by : Keri A. Kornelson

Download or read book Operator Methods in Wavelets, Tilings, and Frames written by Keri A. Kornelson and published by American Mathematical Soc.. This book was released on 2014-10-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13-14, 2013, in Boulder, Colorado. Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more. The papers in this volume touch on a wide variety of topics, including: convex geometry, direct integral decompositions, Beurling density, operator-valued measures, and splines. These varied topics arise naturally in the study of frames in finite and infinite dimensions. In nearly all of the papers, techniques from operator theory serve as crucial tools to solving problems in frame theory. This volume will be of interest not only to researchers in frame theory but also to those in approximation theory, representation theory, functional analysis, and harmonic analysis.

The Averaged Moduli of Smoothness

Author : Blagovest Sendov
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis The Averaged Moduli of Smoothness by : Blagovest Sendov

Download or read book The Averaged Moduli of Smoothness written by Blagovest Sendov and published by . This book was released on 1988 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors outline this new theory of estimating the error in commonly used numerical methods, including interpolation, approximation of function by means of operators and quadrature formulae. The advantage of this theory is that it allows the error to be estimated for an approximation method.

An Integrated Introduction to Computer Graphics and Geometric Modeling

Author : Ronald Goldman
Publisher : CRC Press
ISBN 13 : 1439803358
Total Pages : 592 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis An Integrated Introduction to Computer Graphics and Geometric Modeling by : Ronald Goldman

Download or read book An Integrated Introduction to Computer Graphics and Geometric Modeling written by Ronald Goldman and published by CRC Press. This book was released on 2009-07-14 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with f

Mathematics and Computing

Author : B. Rushi Kumar
Publisher : Springer Nature
ISBN 13 : 9811993076
Total Pages : 701 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Mathematics and Computing by : B. Rushi Kumar

Download or read book Mathematics and Computing written by B. Rushi Kumar and published by Springer Nature. This book was released on 2023-03-14 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6–8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts—applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications—the book is a useful resource for students, researchers and faculty as well as practitioners.

Handbook of Mathematical Geosciences

Author : B.S. Daya Sagar
Publisher : Springer
ISBN 13 : 3319789996
Total Pages : 911 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Handbook of Mathematical Geosciences by : B.S. Daya Sagar

Download or read book Handbook of Mathematical Geosciences written by B.S. Daya Sagar and published by Springer. This book was released on 2018-06-25 with total page 911 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.

Multivariate Approximation and Splines

Author : Günther Nürnberger
Publisher : Birkhäuser
ISBN 13 : 3034888716
Total Pages : 329 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Approximation and Splines by : Günther Nürnberger

Download or read book Multivariate Approximation and Splines written by Günther Nürnberger and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.