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An Integer Number Algorithm To Solve Linear Equations
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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 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 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 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 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 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 A simplified version of H.W. Lenstra's integer programming algorithm and some applications by : A. Paz
Download or read book A simplified version of H.W. Lenstra's integer programming algorithm and some applications written by A. Paz and published by . This book was released on 1983 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very interesting algorithm has been recently suggested by H. W. Lenstra, Jr. [1] for solving integer programming problems. One part of that algorithm was further improved in [2]. The algorithm was shown to be polynomial in the length of the input, for a fixed number of variables. On the other hand the algorithm is impractical for a large number of variables and its implementation is not clear even for a small number of variables. We suggest here a few simplifications and improvements to that algorithm, making its implementation easy (though still impractical for a great number of variables). As a byproduct we show how to solve diophantine linear equations over the nonnegative integers. For a small number of variables (3 or 4) a practical and fast algorithm for solving such equation results.
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 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 Diophantine Equations by : Benne M. M. De Weger
Download or read book Algorithms for Diophantine Equations written by Benne M. M. De Weger and published by . This book was released on 1989 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Number-Theoretic Algorithms in Cryptography by : Oleg Nikolaevich Vasilenko
Download or read book Number-Theoretic Algorithms in Cryptography written by Oleg Nikolaevich Vasilenko and published by American Mathematical Soc.. This book was released on 2007 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important: algorithms for primality testing; factorization algorithms for integers and for polynomials in one variable; applications of the theory of elliptic curves; algorithms for computation of discrete logarithms; algorithms for solving linear equations over finite fields; and, algorithms for performing arithmetic operations on large integers. The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.
Book Synopsis Advances in Cryptology - ASIACRYPT 2008 by : Josef Pawel Pieprzyk
Download or read book Advances in Cryptology - ASIACRYPT 2008 written by Josef Pawel Pieprzyk and published by Springer. This book was released on 2008-12-02 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2008, held in Melbourne, Australia, in December 2008. The 33 revised full papers presented together with the abstract of 1 invited lecture were carefully reviewed and selected from 208 submissions. The papers are organized in topical sections on muliti-party computation, cryptographic protocols, cryptographic hash functions, public-key cryptograhy, lattice-based cryptography, private-key cryptograhy, and analysis of stream ciphers.
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 Methods and Applications of Error-Free Computation by : R. T. Gregory
Download or read book Methods and Applications of Error-Free Computation written by R. T. Gregory and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.
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 Foundations of Algorithms by : Richard Neapolitan
Download or read book Foundations of Algorithms written by Richard Neapolitan and published by Jones & Bartlett Learning. This book was released on 2014-03-05 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Algorithms, Fifth Edition offers a well-balanced presentation of algorithm design, complexity analysis of algorithms, and computational complexity. Ideal for any computer science students with a background in college algebra and discrete structures, the text presents mathematical concepts using standard English and simple notation to maximize accessibility and user-friendliness. Concrete examples, appendices reviewing essential mathematical concepts, and a student-focused approach reinforce theoretical explanations and promote learning and retention. C++ and Java pseudocode help students better understand complex algorithms. A chapter on numerical algorithms includes a review of basic number theory, Euclid's Algorithm for finding the greatest common divisor, a review of modular arithmetic, an algorithm for solving modular linear equations, an algorithm for computing modular powers, and the new polynomial-time algorithm for determining whether a number is prime.The revised and updated Fifth Edition features an all-new chapter on genetic algorithms and genetic programming, including approximate solutions to the traveling salesperson problem, an algorithm for an artificial ant that navigates along a trail of food, and an application to financial trading. With fully updated exercises and examples throughout and improved instructor resources including complete solutions, an Instructor’s Manual and PowerPoint lecture outlines, Foundations of Algorithms is an essential text for undergraduate and graduate courses in the design and analysis of algorithms. Key features include:• The only text of its kind with a chapter on genetic algorithms• Use of C++ and Java pseudocode to help students better understand complex algorithms• No calculus background required• Numerous clear and student-friendly examples throughout the text• Fully updated exercises and examples throughout• Improved instructor resources, including complete solutions, an Instructor’s Manual, and PowerPoint lecture outlines
