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Author: Evar D. Nering
Publisher: Academic Press
ISBN: 9780125154406
Category : Computers
Languages : en
Pages : 618
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Book Description
This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.
Author: Evar D. Nering
Publisher: Academic Press
ISBN: 9780125154406
Category : Computers
Languages : en
Pages : 618
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Book Description
This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.
Author: John A. Trangenstein
Publisher: Springer
ISBN: 3319691058
Category : Mathematics
Languages : en
Pages : 638
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Book Description
This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.
Author: Ivan Stanimirović
Publisher: CRC Press
ISBN: 1000522113
Category : Computers
Languages : en
Pages : 119
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Book Description
This new volume provides the information needed to understand the simplex method, the revised simplex method, dual simplex method, and more for solving linear programming problems. Following a logical order, the book first gives a mathematical model of the linear problem programming and describes the usual assumptions under which the problem is solved. It gives a brief description of classic algorithms for solving linear programming problems as well as some theoretical results. It goes on to explain the definitions and solutions of linear programming problems, outlining the simplest geometric methods and showing how they can be implemented. Practical examples are included along the way. The book concludes with a discussion of multi-criteria decision-making methods. Advances in Optimization and Linear Programming is a highly useful guide to linear programming for professors and students in optimization and linear programming.
Author: Philip N. Klein
Publisher:
ISBN: 9780615856735
Category : Algebras, Linear
Languages : en
Pages : 530
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Book Description
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.
Author: Alain Finkel
Publisher: Springer Science & Business Media
ISBN: 9783540552109
Category : Computers
Languages : ja
Pages : 644
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Book Description
This volume gives the proceedings of the ninth Symposium on Theoretical Aspects of Computer Science (STACS). This annual symposium is held alternately in France and Germany and is organized jointly by the Special Interest Group for Fundamental Computer Science of the Association Francaise des Sciences et Technologies de l'Information et des Syst mes (AFCET) and the Special Interest Group for Theoretical Computer Science of the Gesellschaft f}r Informatik (GI). The volume includes three invited lectures and sections on parallel algorithms, logic and semantics, computational geometry, automata and languages, structural complexity, computational geometry and learning theory, complexity and communication, distributed systems, complexity, algorithms, cryptography, VLSI, words and rewriting, and systems.
Author: Hans Petter Langtangen
Publisher: Springer
ISBN: 3662498871
Category : Computers
Languages : en
Pages : 942
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Book Description
The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015
Author: David Halpern
Publisher: CRC Press
ISBN: 1420035444
Category : Mathematics
Languages : en
Pages : 697
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Book Description
Since its introduction in 1984, MATLAB's ever-growing popularity and functionality have secured its position as an industry-standard software package. The user-friendly, interactive environment of MATLAB 6.x, which includes a high-level programming language, versatile graphics capabilities, and abundance of intrinsic functions, helps users focus on
Author: Mauricio G.C. Resende
Publisher: Springer Science & Business Media
ISBN: 9781402076534
Category : Computers
Languages : en
Pages : 744
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Book Description
Combinatorial optimization is the process of finding the best, or optimal, so lution for problems with a discrete set of feasible solutions. Applications arise in numerous settings involving operations management and logistics, such as routing, scheduling, packing, inventory and production management, lo cation, logic, and assignment of resources. The economic impact of combi natorial optimization is profound, affecting sectors as diverse as transporta tion (airlines, trucking, rail, and shipping), forestry, manufacturing, logistics, aerospace, energy (electrical power, petroleum, and natural gas), telecommu nications, biotechnology, financial services, and agriculture. While much progress has been made in finding exact (provably optimal) so lutions to some combinatorial optimization problems, using techniques such as dynamic programming, cutting planes, and branch and cut methods, many hard combinatorial problems are still not solved exactly and require good heuristic methods. Moreover, reaching "optimal solutions" is in many cases meaningless, as in practice we are often dealing with models that are rough simplifications of reality. The aim of heuristic methods for combinatorial op timization is to quickly produce good-quality solutions, without necessarily providing any guarantee of solution quality. Metaheuristics are high level procedures that coordinate simple heuristics, such as local search, to find solu tions that are of better quality than those found by the simple heuristics alone: Modem metaheuristics include simulated annealing, genetic algorithms, tabu search, GRASP, scatter search, ant colony optimization, variable neighborhood search, and their hybrids.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 464
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Book Description
Author: Peter Bürgisser
Publisher: Springer Science & Business Media
ISBN: 3642388965
Category : Computers
Languages : en
Pages : 567
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Book Description
This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.
