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Algebraic And Algorithmic Aspects Of Differential And Integral Operators


Algebraic And Algorithmic Aspects Of Differential And Integral Operators
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Algebraic And Algorithmic Aspects Of Differential And Integral Operators


Algebraic And Algorithmic Aspects Of Differential And Integral Operators
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Author : Moulay Barkatou
language : en
Publisher: Springer
Release Date : 2014-02-25

Algebraic And Algorithmic Aspects Of Differential And Integral Operators written by Moulay Barkatou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-25 with Computers categories.


This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.



Algebraic And Symbolic Computation Methods In Dynamical Systems


Algebraic And Symbolic Computation Methods In Dynamical Systems
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Author : Alban Quadrat
language : en
Publisher: Springer Nature
Release Date : 2020-05-30

Algebraic And Symbolic Computation Methods In Dynamical Systems written by Alban Quadrat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-30 with Science categories.


This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.



Surveys In Differential Algebraic Equations Ii


Surveys In Differential Algebraic Equations Ii
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Author : Achim Ilchmann
language : en
Publisher: Springer
Release Date : 2014-12-04

Surveys In Differential Algebraic Equations Ii written by Achim Ilchmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-04 with Mathematics categories.


The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Observers for DAEs - DAEs in chemical processes - Optimal control of DAEs - DAEs from a functional-analytic viewpoint - Algebraic methods for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.



Rings Modules And Codes


Rings Modules And Codes
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Author : André Leroy
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-12

Rings Modules And Codes written by André Leroy and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-12 with Mathematics categories.


This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.



D Finite Functions


D Finite Functions
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Author : Manuel Kauers
language : en
Publisher: Springer Nature
Release Date : 2023-11-08

D Finite Functions written by Manuel Kauers and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-08 with Mathematics categories.


Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. This book is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting relations from given data, for evaluating D-finite functions, for executing closure properties, for obtaining various kinds of “explicit” expressions, for factoring operators, and for definite and indefinite symbolic summation and integration are explained in detail. The book comes “with batteries included” in the sense that it requires no background in computer algebra as the relevant facts from this area are summarized in the beginning. This makes the book accessible to a wide range of readers, from mathematics students who plan to work themselves on D-finite functions to researchers who want to apply the theory to their own work. Hundreds of exercises invite the reader to apply the techniques in the book and explore further aspects of the theory on their own. Solutions to all exercises are given in the appendix. When algorithms for D-finite functions came up in the early 1990s, computer proofs were met with a certain skepticism. Fortunately, these times are over and computer algebra has become a standard tool for many mathematicians. Yet, this powerful machinery is still not as widely known as it deserves. This book helps to spread the word that certain tasks can be safely delegated to a computer algebra system, and also what the limitations of these techniques are.



Applied Numerical Linear Algebra


Applied Numerical Linear Algebra
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Author : William W. Hager
language : en
Publisher: SIAM
Release Date : 2022-01-21

Applied Numerical Linear Algebra written by William W. Hager and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-21 with Mathematics categories.


This book introduces numerical issues that arise in linear algebra and its applications. It touches on a wide range of techniques, including direct and iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Detailed explanations on a wide range of topics from condition numbers to singular value decomposition are provided, as well as material on nonlinear and linear systems. Numerical examples, often based on discretizations of boundary-value problems, are used to illustrate concepts. Exercises with detailed solutions are provided at the end of the book, and supplementary material and updates are available online. This Classics edition is appropriate for junior and senior undergraduate students and beginning graduate students in courses such as advanced numerical analysis, special topics on numerical analysis, topics on data science, topics on numerical optimization, and topics on approximation theory.



Linear Algebra For Large Scale And Real Time Applications


Linear Algebra For Large Scale And Real Time Applications
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Author : M.S. Moonen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09

Linear Algebra For Large Scale And Real Time Applications written by M.S. Moonen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.


Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992



Computer Algebra In Quantum Field Theory


Computer Algebra In Quantum Field Theory
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Author : Carsten Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-05

Computer Algebra In Quantum Field Theory written by Carsten Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-05 with Science categories.


The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.



Orthogonal Polynomials


Orthogonal Polynomials
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Author : Mama Foupouagnigni
language : en
Publisher: Springer Nature
Release Date : 2020-03-11

Orthogonal Polynomials written by Mama Foupouagnigni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Mathematics categories.


This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.



Advances In Computer Algebra


Advances In Computer Algebra
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Author : Carsten Schneider
language : en
Publisher: Springer
Release Date : 2018-02-26

Advances In Computer Algebra written by Carsten Schneider and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-26 with Mathematics categories.


This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.