Approximation And Computation

Author : Walter Gautschi,Giuseppe Mastroianni,Themistocles M. Rassias
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 43,8 Mb
Release : 2010-10-20
Category : Mathematics
ISBN : 9781441965943

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Approximation and Computation by Walter Gautschi,Giuseppe Mastroianni,Themistocles M. Rassias Pdf

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.

Author : Marek Kowalski,Christopher Sikorski,Frank Stenger
Publisher : Oxford University Press
Page : 366 pages
File Size : 41,9 Mb
Release : 1995-08-31
Category : Mathematics
ISBN : 9780195359770

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Selected Topics in Approximation and Computation by Marek Kowalski,Christopher Sikorski,Frank Stenger Pdf

Selected Topics in Approximation and Computation addresses the relationship between modern approximation theory and computational methods. The text is a combination of expositions of basic classical methods of approximation leading to popular splines and new explicit tools of computation, including Sinc methods, elliptic function methods, and positive operator approximation methods. It also provides an excellent summary of worst case analysis in information based complexity. It relates optimal computational methods with the theory of s-numbers and n-widths. It can serve as a text for senior-graduate courses in computer science and applied mathematics, and also as a reference for professionals.

Author : Vijay Gupta,Michael Th. Rassias
Publisher : Springer Nature
Page : 107 pages
File Size : 52,8 Mb
Release : 2021-11-29
Category : Mathematics
ISBN : 9783030855635

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Computation and Approximation by Vijay Gupta,Michael Th. Rassias Pdf

This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators. It will be of interest to students both graduate and undergraduate studying linear positive operators and the area of approximation theory.

Author : Marek A. Kowalski,Krzystof A. Sikorski,Frank Stenger
Publisher : Oxford University Press, USA
Page : 366 pages
File Size : 54,9 Mb
Release : 1995-10-19
Category : Mathematics
ISBN : 9780195080599

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Selected Topics in Approximation and Computation by Marek A. Kowalski,Krzystof A. Sikorski,Frank Stenger Pdf

Selected Topics in Approximation and Computation is a combination of expositions of basic classical methods of approximation leading to popular splines and new explicit tools of computation, including sinc methods, elliptic function methods, and positive operator approximation methods. It also provides an excellent summary of worst case analysis in Information Based Complexity. It relates optimal computational methods e=with the theory of s-numbers and m-widths.

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Page : 934 pages
File Size : 40,5 Mb
Release : 2022-05-05
Category : Mathematics
ISBN : 9783030841225

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Approximation and Computation in Science and Engineering by Nicholas J. Daras,Themistocles M. Rassias Pdf

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Author : Charles Stein
Publisher : IMS
Page : 172 pages
File Size : 44,7 Mb
Release : 1986
Category : Mathematics
ISBN : 0940600080

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Approximate Computation of Expectations by Charles Stein Pdf

Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 44,5 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0486640698

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An Introduction to the Approximation of Functions by Theodore J. Rivlin Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Mohammad Monir Uddin
Publisher : CRC Press
Page : 279 pages
File Size : 54,6 Mb
Release : 2019-04-30
Category : Mathematics
ISBN : 9781351028608

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Computational Methods for Approximation of Large-Scale Dynamical Systems by Mohammad Monir Uddin Pdf

These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB® codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.

Author : Marek A. Kowalski,Krzysztof A. Sikorski,Frank Stenger
Publisher : Unknown
Page : 349 pages
File Size : 46,7 Mb
Release : 1995
Category : Approximation theory
ISBN : 0197560407

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Selected Topics in Approximation and Computation by Marek A. Kowalski,Krzysztof A. Sikorski,Frank Stenger Pdf

'Selected Topics in Approximation and Computation' is a combination of expositions of basic classical methods of approximation leading to popular splines and new explicit tools of computation, including sinc methods, elliptic function methods and positive operator approximation methods. It also provides an excellent summary of worst case analysis in information based complexity. It relates optimal computational methods e=with the theory of s-numbers and m-widths.

Author : Domingo Barrera,Sara Remogna,Driss Sbibih
Publisher : Springer
Page : 0 pages
File Size : 40,6 Mb
Release : 2023-05-09
Category : Mathematics
ISBN : 3030943410

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Mathematical and Computational Methods for Modelling, Approximation and Simulation by Domingo Barrera,Sara Remogna,Driss Sbibih Pdf

This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.

Author : Ding-Zhu Du,Jie Wang
Publisher : Springer Nature
Page : 298 pages
File Size : 43,9 Mb
Release : 2020-02-20
Category : Computers
ISBN : 9783030416720

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Complexity and Approximation by Ding-Zhu Du,Jie Wang Pdf

This Festschrift is in honor of Ker-I Ko, Professor in the Stony Brook University, USA. Ker-I Ko was one of the founding fathers of computational complexity over real numbers and analysis. He and Harvey Friedman devised a theoretical model for real number computations by extending the computation of Turing machines. He contributed significantly to advancing the theory of structural complexity, especially on polynomial-time isomorphism, instance complexity, and relativization of polynomial-time hierarchy. Ker-I also made many contributions to approximation algorithm theory of combinatorial optimization problems. This volume contains 17 contributions in the area of complexity and approximation. Those articles are authored by researchers over the world, including North America, Europe and Asia. Most of them are co-authors, colleagues, friends, and students of Ker-I Ko.

Author : Ioannis C. Demetriou,Panos M. Pardalos
Publisher : Springer
Page : 237 pages
File Size : 52,9 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9783030127671

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Approximation and Optimization by Ioannis C. Demetriou,Panos M. Pardalos Pdf

This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29–30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning ; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 48,5 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

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Mathematics and Computation by Avi Wigderson Pdf

An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Author : J. Haslinger,R. A. E. Makinen
Publisher : SIAM
Page : 276 pages
File Size : 41,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9780898715361

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Introduction to Shape Optimization by J. Haslinger,R. A. E. Makinen Pdf

Treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory through computational aspects to industrial applications.

Author : Richard S. Varga
Publisher : SIAM
Page : 128 pages
File Size : 44,9 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 1611970113

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Scientific Computation on Mathematical Problems and Conjectures by Richard S. Varga Pdf

Studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques. The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures. Scientific Computation on Mathematical Problems and Conjectures includes studies of the Bernstein Conjecture of 1913 in polynomial approximation theory, the "1/9" Conjecture of 1977 in rational approximation theory, the famous Riemann Hypothesis of 1859, and the Polya Conjecture of 1927. The emphasis of this monograph rests strongly on the interplay between hard analysis and high-precision calculations.