On The Complexity Of Composition And Generalized Composition Of Power Series
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A General Theory Of Optimal Algorithms
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Author : Joseph Frederick Traub
language : en
Publisher:
Release Date : 1980
A General Theory Of Optimal Algorithms written by Joseph Frederick Traub and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
The purpose of this monograph is to create a general framework for the study of optimal algorithms for problems that are solved approximately. For generality the setting is abstract, but we present many applications to practical problems and provide examples to illustrate concepts and major theorems. The work presented here is motivated by research in many fields. Influential have been questions, concepts, and results from complexity theory, algorithmic analysis, applied mathematics and numerical analysis, the mathematical theory of approximation (particularly the work on n-widths in the sense of Gelfand and Kolmogorov), applied approximation theory (particularly the theory of splines), as well as earlier work on optimal algorithms. But many of the questions we ask (see Overview) are new. We present a different view of algorithms and complexity and must request the reader's
Applied And Computational Complex Analysis Volume 3
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Author : Peter Henrici
language : en
Publisher: John Wiley & Sons
Release Date : 1993-04-16
Applied And Computational Complex Analysis Volume 3 written by Peter Henrici and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-16 with Mathematics categories.
Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.
On The Complexity Of Composition And Generalized Composition Of Power Series
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1978
On The Complexity Of Composition And Generalized Composition Of Power Series written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algorithms categories.
Let F(x) = f1x + f2(x)(x) + ... be a formal power series over a field Delta. Let F superscript 0(x) = x and for q = 1,2, ..., define F superscript q(x) = F superscript (q-1) (F(x)). The obvious algorithm for computing the first n terms of F superscript q(x) is by the composition position analogue of repeated squaring. This algorithm has complexity about log 2 q times that of a single composition. The factor log 2 q can be eliminated in the computation of the first n terms of (F(x)) to the q power by a change of representation, using the logarithm and exponential functions. We show the factor log 2 q can also be eliminated for the composition problem. F superscript q(x) can often, but not always, be defined for more general q. We give algorithms and complexity bounds for computing the first n terms of F superscript q(x) whenever it is defined.
Siam Journal On Computing
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Author : Society for Industrial and Applied Mathematics
language : en
Publisher:
Release Date : 1980
Siam Journal On Computing written by Society for Industrial and Applied Mathematics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Computer programming categories.
Topics In Computational Complexity And The Analysis Of Algorithms
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1980
Topics In Computational Complexity And The Analysis Of Algorithms written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Algorithms categories.
Selected Works Of Richard P Stanley
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Author : Victor Reiner
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-17
Selected Works Of Richard P Stanley written by Victor Reiner 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 2017-05-17 with Mathematics categories.
Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Polynomial And Matrix Computations
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Author : Dario Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Polynomial And Matrix Computations written by Dario Bini 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 2012-12-06 with Mathematics categories.
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.
Algebraic Complexity Theory
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Author : Peter Bürgisser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebraic Complexity Theory written by Peter Bürgisser 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 2013-03-14 with Mathematics categories.
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.
Modern Computer Arithmetic
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Author : Richard P. Brent
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-25
Modern Computer Arithmetic written by Richard P. Brent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Computers categories.
Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.