Algorithms As A Basis Of Modern Applied Mathematics

Author : Šárka Hošková-Mayerová,Cristina Flaut,Fabrizio Maturo
Publisher : Springer Nature
Page : 515 pages
File Size : 46,8 Mb
Release : 2021-01-13
Category : Technology & Engineering
ISBN : 9783030613341

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Algorithms as a Basis of Modern Applied Mathematics by Šárka Hošková-Mayerová,Cristina Flaut,Fabrizio Maturo Pdf

This book offers a self-contained guide to advanced algorithms and their applications in various fields of science. Gathering contributions by authoritative researchers in the field of mathematics, statistics and computer science, it aims at offering a comprehensive and up-to-date view of algorithms, including the theory behind them, as well as practical considerations, current limitations and solutions. It covers applications in energy management, decision making, computer networks, materials science, mechanics and process optimization. It offers an integrated and timely guide to important algorithms, and represents a valuable reference resource for graduate students and researchers in various fields of applied mathematics, statistics and engineering.

Author : Jeffrey Humpherys,Tyler J. Jarvis
Publisher : SIAM
Page : 806 pages
File Size : 53,8 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9781611976069

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Foundations of Applied Mathematics, Volume 2 by Jeffrey Humpherys,Tyler J. Jarvis Pdf

In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization. When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?” This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, and machine learning.

Author : Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Publisher : SIAM
Page : 709 pages
File Size : 47,9 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9781611974904

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Foundations of Applied Mathematics, Volume I by Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans Pdf

This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis?includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

Author : Kenneth Lange
Publisher : SIAM
Page : 227 pages
File Size : 46,6 Mb
Release : 2020-05-04
Category : Mathematics
ISBN : 9781611976175

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Algorithms from THE BOOK by Kenneth Lange Pdf

Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Written in clear, instructive language within the constraints of mathematical rigor, Algorithms from THE BOOK includes a large number of classroom-tested exercises at the end of each chapter. The appendices cover background material often omitted from undergraduate courses. Most of the algorithm descriptions are accompanied by Julia code, an ideal language for scientific computing. This code is immediately available for experimentation. Algorithms from THE BOOK is aimed at first-year graduate and advanced undergraduate students. It will also serve as a convenient reference for professionals throughout the mathematical sciences, physical sciences, engineering, and the quantitative sectors of the biological and social sciences.

Author : JEFFREY. JARVIS HUMPHERYS (TYLER J.)
Publisher : Unknown
Page : 128 pages
File Size : 49,8 Mb
Release : 2020
Category : Electronic
ISBN : 1611976057

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FOUNDATIONS OF APPLIED MATHEMATICS, VOLUME 2 by JEFFREY. JARVIS HUMPHERYS (TYLER J.) Pdf

Author : Daniele Gardy,Abdelkader Mokkadem
Publisher : Birkhäuser
Page : 337 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884051

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Mathematics and Computer Science by Daniele Gardy,Abdelkader Mokkadem Pdf

This is the first book where mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep mathematical approaches. It contains a collection of refereed papers presented at the Colloquium on Mathematics and Computer Science held at the University of Versailles-St-Quentin on September 18-20, 2000. The colloquium was a meeting place for researchers in mathematics and computer science and thus an important opportunity to exchange ideas and points of view, and to present new approaches and new results in the common areas such as algorithms analysis, trees, combinatorics, optimization, performance evaluation and probabilities. The book is intended for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and related modern mathematical methods. The range of applications is very wide and reaches beyond computer science.

Author : Fred J. Hickernell,Peter Kritzer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 200 pages
File Size : 47,9 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110633153

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Multivariate Algorithms and Information-Based Complexity by Fred J. Hickernell,Peter Kritzer Pdf

The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.

Author : Armin Iske,Jeremy Levesley
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 53,6 Mb
Release : 2006-12-13
Category : Mathematics
ISBN : 9783540465515

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Algorithms for Approximation by Armin Iske,Jeremy Levesley Pdf

Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.

Author : Vladimir Uspensky,A. L. Semenov
Publisher : Unknown
Page : 284 pages
File Size : 51,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401582335

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Algorithms by Vladimir Uspensky,A. L. Semenov Pdf

Author : S. D. Conte,Carl De Boor
Publisher : SIAM
Page : 474 pages
File Size : 41,5 Mb
Release : 2018-02-27
Category : Science
ISBN : 9781611975208

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Elementary Numerical Analysis by S. D. Conte,Carl De Boor Pdf

This book provides a thorough and careful introduction to the theory and practice of scientific computing at an elementary, yet rigorous, level, from theory via examples and algorithms to computer programs. The original FORTRAN programs have been rewritten in MATLAB and now appear in a new appendix and online, offering a modernized version of this classic reference for basic numerical algorithms.

Author : Alena Vagaská,Miroslav Gombár,Anton Panda
Publisher : Springer Nature
Page : 181 pages
File Size : 51,9 Mb
Release : 2023-07-20
Category : Technology & Engineering
ISBN : 9783031353390

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Optimization Methods in Mathematical Modeling of Technological Processes by Alena Vagaská,Miroslav Gombár,Anton Panda Pdf

This book focuses on selected methods of applied mathematics that are aimed at mathematical optimization, with an emphasis on their application in engineering practice. It delves into the current mathematical modeling of processes and systems, with a specific focus on the optimization modeling of technological processes. The authors discuss suitable linear, convex, and nonlinear optimization methods for solving problems in engineering practice. Real-world examples and data are used to numerically illustrate the implementation of these methods, utilizing the popular MATLAB software system and its extension to convex optimization. The book covers a wide range of topics, including mathematical modeling, linear programming, convex programming, and nonlinear programming, all with an engineering optimization perspective. It serves as a comprehensive guide for engineers, researchers, and students interested in the practical application of optimization methods in engineering.

Author : Sergiy A. Plaksa,Vitalii S. Shpakivskyi
Publisher : Springer Nature
Page : 548 pages
File Size : 42,9 Mb
Release : 2023-07-18
Category : Mathematics
ISBN : 9783031322549

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Monogenic Functions in Spaces with Commutative Multiplication and Applications by Sergiy A. Plaksa,Vitalii S. Shpakivskyi Pdf

This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.

Author : Ivan V. Sergienko,Valeriy K. Zadiraka,Oleg M. Lytvyn
Publisher : Springer Nature
Page : 387 pages
File Size : 53,7 Mb
Release : 2022-01-11
Category : Mathematics
ISBN : 9783030909086

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Elements of the General Theory of Optimal Algorithms by Ivan V. Sergienko,Valeriy K. Zadiraka,Oleg M. Lytvyn Pdf

In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.

Author : Anatoly B. Bakushinsky,Mikhail M. Kokurin,Mikhail Yu. Kokurin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 43,5 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110556384

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Regularization Algorithms for Ill-Posed Problems by Anatoly B. Bakushinsky,Mikhail M. Kokurin,Mikhail Yu. Kokurin Pdf

This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems

Author : Michael T. Heath
Publisher : SIAM
Page : 567 pages
File Size : 48,6 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9781611975581

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Scientific Computing by Michael T. Heath Pdf

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.