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Integer Algorithms To Solve Linear Equations And Systems
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Book Synopsis INTEGER ALGORITHMS TO SOLVE LINEAR EQUATIONS AND SYSTEMS by : Florentin Smarandache
Download or read book INTEGER ALGORITHMS TO SOLVE LINEAR EQUATIONS AND SYSTEMS written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two algorithms for solving Diophantine linear equations and five algorithms for solving Diophantine linear systems, together with many examples, are presented in this paper.
Book Synopsis Five Integer Number Algorithms To Solve Linear Systems by : FLORENTIN SMARANDACHE
Download or read book Five Integer Number Algorithms To Solve Linear Systems written by FLORENTIN SMARANDACHE and published by Infinite Study. This book was released on with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This section further extends the results obtained in chapters 4 and 5 (from linear equation to linear systems). Each algorithm is thoroughly proved and then an example is given.
Book Synopsis ALGORITHMS FOR SOLVING LINEAR CONGRUENCES AND SYSTEMS OF LINEAR CONGRUENCES by : Florentin Smarandache
Download or read book ALGORITHMS FOR SOLVING LINEAR CONGRUENCES AND SYSTEMS OF LINEAR CONGRUENCES written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences and we find the number of distinct solutions. Many examples of solving congruences are given.
Book Synopsis Another Integer Algorithm To Solve Linear Equations (Using Congruences) by : FLORENTIN SMARANDACHE
Download or read book Another Integer Algorithm To Solve Linear Equations (Using Congruences) written by FLORENTIN SMARANDACHE and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this section is presented a new integer number algorithm for linear equation. This algorithm is more “rapid” than W. Sierpinski’s presented in [1] in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.
Book Synopsis An Integer Number Algorithm To Solve Linear Equations by : FLORENTIN SMARANDACHE
Download or read book An Integer Number Algorithm To Solve Linear Equations written by FLORENTIN SMARANDACHE and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: An algorithm is given that ascertains whether a linear equation has integer number solutions or not; if it does, the general integer solution is determined.
Book Synopsis Computer Algorithms for Solving Linear Algebraic Equations by : Emilio Spedicato
Download or read book Computer Algorithms for Solving Linear Algebraic Equations written by Emilio Spedicato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on "Computer algorithms for solving linear algebraic equations: the state of the art" was held September 9-21, 1990, at II Ciocco, Barga, Italy. It was attended by 68 students (among them many well known specialists in related fields!) from the following countries: Belgium, Brazil, Canada, Czechoslovakia, Denmark, France, Germany, Greece, Holland, Hungary, Italy, Portugal, Spain, Turkey, UK, USA, USSR, Yugoslavia. Solving linear equations is a fundamental task in most of computational mathematics. Linear systems which are now encountered in practice may be of very large dimension and their solution can still be a challenge in terms of the requirements of accuracy or reasonable computational time. With the advent of supercomputers with vector and parallel features, algorithms which were previously formulated in a framework of sequential operations often need a completely new formulation, and algorithms that were not recommended in a sequential framework may become the best choice. The aim of the ASI was to present the state of the art in this field. While not all important aspects could be covered (for instance there is no presentation of methods using interval arithmetic or symbolic computation), we believe that most important topics were considered, many of them by leading specialists who have contributed substantially to the developments in these fields.
Book Synopsis ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) by : Florentin Smarandache
Download or read book ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this section is presented a new integer number algorithm for linear equation. This algorithm is more “rapid” than W. Sierpinski’s presented in in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.
Book Synopsis Theory of Linear and Integer Programming by : Alexander Schrijver
Download or read book Theory of Linear and Integer Programming written by Alexander Schrijver and published by John Wiley & Sons. This book was released on 1998-06-11 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.
Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin
Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.
Book Synopsis Algorithms for Exact Solution of Systems of Linear Equations with Polynomial Coefficients by : Michael Terence McClellan
Download or read book Algorithms for Exact Solution of Systems of Linear Equations with Polynomial Coefficients written by Michael Terence McClellan and published by . This book was released on 1971 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An interval algorithm for solving systems of linear equations to prespecified accuracy by : James W. Demmel
Download or read book An interval algorithm for solving systems of linear equations to prespecified accuracy written by James W. Demmel and published by . This book was released on 1983 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe an interval arithmetic algorithm for solving a special class of simulataneous linear equations. This class includes but is not limited to systems Ax=b where A and b have integer entries. The algorithm uses fixed point arithemetic, and has two properties which distinguish it from earlier algorithms: given the absolute accuracy e desired, the algorithm uses only as much precision as needed to achieve it, and the algorithm can adjust its own parameters to minimize computation time.
Book Synopsis Linear Integer Programming by : Elias Munapo
Download or read book Linear Integer Programming written by Elias Munapo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic equation (CE), application of CE to bi-objective and multi-objective problems, Binary integer problems, Mixed-integer models, Knapsack models, Complexity reduction, Feasible-space reduction, Random search, Connected graph are also treated.
Book Synopsis Computer Solution of Large Linear Systems by : Gerard Meurant
Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Book Synopsis Algorithms for the Solution of Systems of Linear Diophantine Equations by : Joseph Tsu-wu Chou
Download or read book Algorithms for the Solution of Systems of Linear Diophantine Equations written by Joseph Tsu-wu Chou and published by . This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Collected Papers. Volume I by : Florentin Smarandache
Download or read book Collected Papers. Volume I written by Florentin Smarandache and published by Infinite Study. This book was released on 2007-01-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles, notes, generalizations, paradoxes, miscellaneous in mathematics, linguistics, and education.
Book Synopsis Sparse Solutions of Underdetermined Linear Systems and Their Applications by : Ming-Jun Lai
Download or read book Sparse Solutions of Underdetermined Linear Systems and Their Applications written by Ming-Jun Lai and published by SIAM. This book was released on 2021-06-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a special solution to underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called a sparse solution. Since underdetermined linear systems can be very different, the authors explain how to compute a sparse solution using many approaches. Sparse Solutions of Underdetermined Linear Systems and Their Applications contains 64 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval and provides a detailed explanation of these algorithms including derivations and convergence analysis. Exercises for each chapter help readers understand the material. This textbook is appropriate for graduate students in math and applied math, computer science, statistics, data science, and engineering. Advisors and postdoctoral scholars will also find the book interesting and useful.
Book Synopsis Linear and Integer Programming Made Easy by : T. C. Hu
Download or read book Linear and Integer Programming Made Easy written by T. C. Hu and published by Springer. This book was released on 2016-05-03 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides concise coverage of the basics of linear and integer programming which, with megatrends toward optimization, machine learning, big data, etc., are becoming fundamental toolkits for data and information science and technology. The authors’ approach is accessible to students from almost all fields of engineering, including operations research, statistics, machine learning, control system design, scheduling, formal verification and computer vision. The presentations enables the basis for numerous approaches to solving hard combinatorial optimization problems through randomization and approximation. Readers will learn to cast various problems that may arise in their research as optimization problems, understand the cases where the optimization problem will be linear, choose appropriate solution methods and interpret results appropriately.
