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Author : George A. Anastassiou,Svetlozar T. Rachev
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461524946
Proceedings of a conference held in Santa Barbara, California, May 20-22, 1993
Author : Louis H.Y. Chen,Larry Goldstein,Qi-Man Shao
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 54,8 Mb
Release : 2010-10-13
Category : Mathematics
ISBN : 9783642150074
Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Author : Radu Paltanea
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 48,8 Mb
Release : 2004-09-17
Category : Mathematics
ISBN : 0817643508
Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results
Author : George A. Anastassiou,Sorin Gal
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 40,9 Mb
Release : 1999-12-22
Category : Mathematics
ISBN : 0817641513
We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.
Author : George A. Anastassiou
Publisher : Springer
Page : 347 pages
File Size : 40,6 Mb
Release : 2018-12-07
Category : Technology & Engineering
ISBN : 9783030042875
Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.
Author : Vydas Čekanavičius
Publisher : Springer
Page : 274 pages
File Size : 47,6 Mb
Release : 2016-06-16
Category : Mathematics
ISBN : 9783319340722
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Author : Michael Luby,Jose Rolim,Maria Serna
Publisher : Springer
Page : 394 pages
File Size : 41,7 Mb
Release : 2003-05-20
Category : Computers
ISBN : 9783540495437
This book constitutes the refereed proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM'98, held in Barcelona, Spain, in October 1998. The 26 revised full papers presented were carefully reviewed and selected for inclusion in the proceedings. Also included are three invited contributions. Among the topics addressed are graph computation, derandomization, pattern matching, computational geometry, approximation algorithms, search algorithms, sorting, and networking algorithms.
Author : George Anastassiou
Publisher : CRC Press
Page : 413 pages
File Size : 49,9 Mb
Release : 2019-06-03
Category : Mathematics
ISBN : 9780429525117
Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f
Author : B. Grigelionis,J. Kubilius,V. Paulauskas,H. Pragarauskas,R. Rudzkis,V. Statulevičius
Publisher : Walter de Gruyter GmbH & Co KG
Page : 752 pages
File Size : 54,8 Mb
Release : 2020-05-05
Category : Mathematics
ISBN : 9783112313480
No detailed description available for "Probability Theory and Mathematical Statistics".
Author : Quan-Lin Li,Jinting Wang,Hai-Bo Yu
Publisher : Springer Nature
Page : 497 pages
File Size : 42,7 Mb
Release : 2019-10-21
Category : Computers
ISBN : 9789811508646
This book is dedicated to Jinhua Cao on the occasion of his 80th birthday. Jinhua Cao is one of the most famous reliability theorists. His main contributions include: published over 100 influential scientific papers; published an interesting reliability book in Chinese in 1986, which has greatly influenced the reliability of education, academic research and engineering applications in China; initiated and organized Reliability Professional Society of China (the first part of Operations Research Society of China) since 1981. The high admiration that Professor Cao enjoys in the reliability community all over the world was witnessed by the enthusiastic response of each contributor in this book. The contributors are leading researchers with diverse research perspectives. The research areas of the book iclude a broad range of topics related to reliability models, queueing theory, manufacturing systems, supply chain finance, risk management, Markov decision processes, blockchain and so forth. The book consists of a brief Preface describing the main achievements of Professor Cao; followed by congratulations from Professors Way Kuo and Wei Wayne Li, and by Operations Research Society of China, and Reliability Professional Society of China; and further followed by 25 articles roughly grouped together. Most of the articles are written in a style understandable to a wide audience. This book is useful to anyone interested in recent developments in reliability, network security, system safety, and their stochastic modeling and analysis.
Author : Andrew Barbour,Hock Peng Chan,David Siegmund
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 55,7 Mb
Release : 2011-12-08
Category : Mathematics
ISBN : 9781461419662
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Author : Mangey Ram,Tadashi Dohi
Publisher : CRC Press
Page : 218 pages
File Size : 48,6 Mb
Release : 2019-04-18
Category : Science
ISBN : 9781351056458
A substantial amount of research has been conducted on consecutive k-out-of-n and related reliability systems over the past four decades. These systems have been used to model various engineering systems such as the microwave stations of telecoms network, oil pipeline systems, and vacuum systems in an electron accelerator. As such, studies of reliability properties of consecutive k-out-of-n structures have attracted significant attention from both theoretical and practical approaches. In the modern era of technology, the redundancies are employed in the various industrial systems to prevent them from failure/sudden failure or to recover from failures. This book is meant to provide knowledge and help engineers and academicians in understanding reliability engineering by using k-out-of-n structures. The material is also targeted at postgraduate or senior undergraduate students pursuing reliability engineering.
Author : Leslie Ann Goldberg,Klaus Jansen,R. Ravi,José D.P. Rolim
Publisher : Springer Science & Business Media
Page : 715 pages
File Size : 41,6 Mb
Release : 2011-08-05
Category : Computers
ISBN : 9783642229343
This book constitutes the joint refereed proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011, and the 15th International Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, USA, in August 2011. The volume presents 29 revised full papers of the APPROX 2011 workshop, selected from 66 submissions, and 29 revised full papers of the RANDOM 2011 workshop, selected from 64 submissions. They were carefully reviewed and selected for inclusion in the book. In addition two abstracts of invited talks are included. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
Author : Olav Kallenberg
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 52,8 Mb
Release : 2002-01-08
Category : Mathematics
ISBN : 0387953132
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Author : George A. Anastassiou
Publisher : Chapman and Hall/CRC
Page : 624 pages
File Size : 51,7 Mb
Release : 2000
Category : Approximation theory
ISBN : 0429181795
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert.Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers.The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.