Contemporary Computational Mathematics A Celebration Of The 80th Birthday Of Ian Sloan

Author : Josef Dick,Frances Y. Kuo,Henryk Woźniakowski
Publisher : Springer
Page : 1309 pages
File Size : 51,6 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319724560

Get Book

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan by Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Pdf

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Author : Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo
Publisher : Springer Nature
Page : 662 pages
File Size : 54,8 Mb
Release : 2021-08-10
Category : Mathematics
ISBN : 9783030774974

Get Book

Weighted Polynomial Approximation and Numerical Methods for Integral Equations by Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo Pdf

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

Author : Bruno Tuffin,Pierre L'Ecuyer
Publisher : Springer Nature
Page : 533 pages
File Size : 47,7 Mb
Release : 2020-05-01
Category : Computers
ISBN : 9783030434656

Get Book

Monte Carlo and Quasi-Monte Carlo Methods by Bruno Tuffin,Pierre L'Ecuyer Pdf

​This book presents the refereed proceedings of the 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Rennes, France, and organized by Inria, in July 2018. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.

Author : Hemen Dutta
Publisher : American Mathematical Society
Page : 256 pages
File Size : 43,7 Mb
Release : 2023-06-12
Category : Mathematics
ISBN : 9781470469641

Get Book

Mathematical Modelling by Hemen Dutta Pdf

This volume is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts. The companion volume (Contemporary Mathematics, Volume 787) is devoted to theory and application.

Author : Dmitriy Bilyk,Josef Dick,Friedrich Pillichshammer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 225 pages
File Size : 49,9 Mb
Release : 2020-01-20
Category : Mathematics
ISBN : 9783110652581

Get Book

Discrepancy Theory by Dmitriy Bilyk,Josef Dick,Friedrich Pillichshammer Pdf

The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.

Author : Joachim Gwinner,Ernst Peter Stephan
Publisher : Springer
Page : 661 pages
File Size : 52,7 Mb
Release : 2018-07-28
Category : Mathematics
ISBN : 9783319920016

Get Book

Advanced Boundary Element Methods by Joachim Gwinner,Ernst Peter Stephan Pdf

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications. Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research. The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Author : Alexander Keller
Publisher : Springer Nature
Page : 315 pages
File Size : 50,7 Mb
Release : 2022-05-20
Category : Mathematics
ISBN : 9783030983192

Get Book

Monte Carlo and Quasi-Monte Carlo Methods by Alexander Keller Pdf

This volume presents the revised papers of the 14th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2020, which took place online during August 10-14, 2020. This book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in statistics, machine learning, finance, and computer graphics, offering information on the latest developments in Monte Carlo and quasi-Monte Carlo methods and their randomized versions.

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 48,8 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

Get Book

Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Author : Wolfgang Hackbusch
Publisher : Springer Nature
Page : 605 pages
File Size : 55,8 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9783030355548

Get Book

Tensor Spaces and Numerical Tensor Calculus by Wolfgang Hackbusch Pdf

Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Author : Kendall Atkinson,David Chien,Olaf Hansen
Publisher : CRC Press
Page : 184 pages
File Size : 40,9 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781000725988

Get Book

Spectral Methods Using Multivariate Polynomials On The Unit Ball by Kendall Atkinson,David Chien,Olaf Hansen Pdf

Spectral Methods Using Multivariate Polynomials on the Unit Ball is a research level text on a numerical method for the solution of partial differential equations. The authors introduce, illustrate with examples, and analyze 'spectral methods' that are based on multivariate polynomial approximations. The method presented is an alternative to finite element and difference methods for regions that are diffeomorphic to the unit disk, in two dimensions, and the unit ball, in three dimensions. The speed of convergence of spectral methods is usually much higher than that of finite element or finite difference methods. Features Introduces the use of multivariate polynomials for the construction and analysis of spectral methods for linear and nonlinear boundary value problems Suitable for researchers and students in numerical analysis of PDEs, along with anyone interested in applying this method to a particular physical problem One of the few texts to address this area using multivariate orthogonal polynomials, rather than tensor products of univariate polynomials.

Author : Tatsien Li
Publisher : Springer Nature
Page : 199 pages
File Size : 45,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789819709922

Get Book

Synchronization for Wave Equations with Locally Distributed Controls by Tatsien Li Pdf

Author : Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster
Publisher : SIAM
Page : 310 pages
File Size : 40,5 Mb
Release : 2022-02-16
Category : Mathematics
ISBN : 9781611976885

Get Book

Sparse Polynomial Approximation of High-Dimensional Functions by Ben Adcock ,Simone Brugiapaglia,Clayton G. Webster Pdf

Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.

Author : Andries E. Brouwer,H. Van Maldeghem
Publisher : Unknown
Page : 481 pages
File Size : 42,9 Mb
Release : 2022-01-13
Category : Language Arts & Disciplines
ISBN : 9781316512036

Get Book

Strongly Regular Graphs by Andries E. Brouwer,H. Van Maldeghem Pdf

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

Author : Mehmet Yavuz,Necati Özdemir
Publisher : Bentham Science Publishers
Page : 275 pages
File Size : 44,7 Mb
Release : 2022-12-14
Category : Mathematics
ISBN : 9789815051940

Get Book

Fractional Calculus: New Applications in Understanding Nonlinear Phenomena by Mehmet Yavuz,Necati Özdemir Pdf

In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been intensively studied formodelling and analysing real-world phenomena. There is now a growing body of research on new methods to understand natural occurrences and tackle different problems. This book presents ten reviews of recent fractional operators split over three sections: 1. Chaotic Systems and Control (covers the Caputo fractional derivative, and a chaotic fractional-order financial system)2. Heat Conduction (covers the Duhamel theorem for time-dependent source terms, and the Cattaneo–Hristov model for oscillatory heat transfer)3. Computational Methods and Their Illustrative Applications (covers mathematical analysis for understanding 5 real-word phenomena: HTLV-1 infection of CD4+ T-cells, traveling waves, rumor-spreading, biochemical reactions, and the computational fluid dynamics of a non-powered floating object navigating in an approach channel) This volume is a resource for researchers in physics, biology, behavioral sciences, and mathematics who are interested in new applications of fractional calculus in the study of nonlinear phenomena.

Author : Giacomo Albi,Sara Merino-Aceituno,Alessia Nota,Mattia Zanella
Publisher : Springer Nature
Page : 251 pages
File Size : 51,7 Mb
Release : 2021-07-15
Category : Science
ISBN : 9783030671044

Get Book

Trails in Kinetic Theory by Giacomo Albi,Sara Merino-Aceituno,Alessia Nota,Mattia Zanella Pdf

In recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School “Trails in Kinetic Theory: Foundational Aspects and Numerical Methods”, hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program “Kinetic Theory”. Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.