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Author : Allan Borodin
Publisher :
ISBN 13 : 9780608163741
Total Pages : 174 pages
Book Rating : 4.1/5 (637 download)
Download or read book The Computational Complexity of Algebraic and Numeric Problems written by Allan Borodin and published by . This book was released on 1990 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Allen Borodin
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (18 download)
Download or read book The Computational Complexity of Algebraic and Numeric Problems written by Allen Borodin and published by . This book was released on 1988 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Allan Borodin
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (493 download)
Download or read book The Computational Complexity of Algebraic and Numeric Problems written by Allan Borodin and published by . This book was released on 1990 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Silvana Ilie
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (16 download)
Download or read book Computational Complexity of Numerical Solutions of Initial Value Problems for Differential Algebraic Equations written by Silvana Ilie and published by . This book was released on 2005 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lenore Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461207010
Total Pages : 456 pages
Book Rating : 4.4/5 (612 download)
Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
Author : Peter Bürgisser
Publisher : Springer Science & Business Media
ISBN 13 : 3662033380
Total Pages : 630 pages
Book Rating : 4.6/5 (62 download)
Download or read book Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Author : Zeke Wang
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.3/5 (91 download)
Download or read book Algebraic Systems of Equations and Computational Complexity Theory written by Zeke Wang and published by . This book was released on 1994 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant progress has been made during the last 15 years in the solution of nonlinear systems, particularly in computing fixed points, solving systems of nonlinear equations and applications to equilibrium models.
Author : Andrei N. Borodin
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (859 download)
Download or read book The Computational Complexity of Algebraic and Nimeric Problems written by Andrei N. Borodin and published by . This book was released on 1975 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3662029456
Total Pages : 556 pages
Book Rating : 4.6/5 (62 download)
Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Author : H. T. Kung
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (82 download)
Download or read book The computational Complexity of algebraic numbers written by H. T. Kung and published by . This book was released on 1973 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The effort required to approximate an algebraic number should increase with its degree. In this paper the assertion is proven in a precise sense. The author shows that the optimal efficiency of approximation can be achieved only for algebraic numbers which have very low degrees; in fact, degree one or degree two.
Author : Eric Bach
Publisher : MIT Press
ISBN 13 : 9780262024051
Total Pages : 536 pages
Book Rating : 4.0/5 (24 download)
Download or read book Algorithmic Number Theory: Efficient algorithms written by Eric Bach and published by MIT Press. This book was released on 1996 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1.
Author : Chee-Keng Yap
Publisher : Oxford University Press on Demand
ISBN 13 : 9780195125160
Total Pages : 511 pages
Book Rating : 4.1/5 (251 download)
Download or read book Fundamental Problems of Algorithmic Algebra written by Chee-Keng Yap and published by Oxford University Press on Demand. This book was released on 2000 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics. Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features · Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system · Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor · Aims to be self-contained in its mathematical development · Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students
Author : Gérard Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 9783540601142
Total Pages : 504 pages
Book Rating : 4.6/5 (11 download)
Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Gérard Cohen and published by Springer Science & Business Media. This book was released on 1995 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.
Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Author : Dario Bini
Publisher : Springer Science & Business Media
ISBN 13 : 1461202655
Total Pages : 433 pages
Book Rating : 4.4/5 (612 download)
Download or read book Polynomial and Matrix Computations written by Dario Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.
Author : Nicola Santoro
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (879 download)
Download or read book The Computational Complexity of Arithmetic and Non Numeric Problems written by Nicola Santoro and published by . This book was released on 1976 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.F. Traub
Publisher : Academic Press
ISBN 13 : 1483257894
Total Pages : 250 pages
Book Rating : 4.4/5 (832 download)
Download or read book Analytic Computational Complexity written by J.F. Traub and published by Academic Press. This book was released on 2014-05-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Computational Complexity contains the proceedings of the Symposium on Analytic Computational Complexity held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7-8, 1975. The symposium provided a forum for assessing progress made in analytic computational complexity and covered topics ranging from strict lower and upper bounds on iterative computational complexity to numerical stability of iterations for solution of nonlinear equations and large linear systems. Comprised of 14 chapters, this book begins with an introduction to analytic computational complexity before turning to proof techniques used in analytic complexity. Subsequent chapters focus on the complexity of obtaining starting points for solving operator equations by Newton's method; maximal order of multipoint iterations using n evaluations; the use of integrals in the solution of nonlinear equations in N dimensions; and the complexity of differential equations. Algebraic constructions in an analytic setting are also discussed, along with the computational complexity of approximation operators. This monograph will be of interest to students and practitioners in the fields of applied mathematics and computer science.
