Fast Algorithms For Manipulating Formal 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
Nasa Conference Publication
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Author :
language : en
Publisher:
Release Date : 1977
Nasa Conference Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Aeronautics categories.
Proceedings Of The 1977 Macsyma Users Conference
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Author :
language : en
Publisher:
Release Date : 1977
Proceedings Of The 1977 Macsyma Users Conference written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Algebra categories.
Algorithms Esa 2004
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Author : Susanne Albers
language : en
Publisher: Springer
Release Date : 2004-09-01
Algorithms Esa 2004 written by Susanne Albers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-01 with Computers categories.
This book constitutes the refereed proceedings of the 12th Annual European Symposium on Algorithms, ESA 2004, held in Bergen, Norway, in September 2004. The 70 revised full papers presented were carefully reviewed from 208 submissions. The scope of the papers spans the entire range of algorithmics from design and mathematical issues to real-world applications in various fields, and engineering and analysis of algorithms.
Fast Algorithms For Manipulating Formal Power Series
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1976
Fast Algorithms For Manipulating Formal 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 1976 with Algorithms categories.
The classical algorithms require O(n sup 3) operations to compute the first n terms in the reversion of a power series or the composition of two series, and O((n sup 2) log n) operations if the fast Fourier transform is used for power series multiplication. In this paper we show that the composition and reversion problems are equivalent (up to constant factors), and we give algorithms which require only O((n log n) sup 3/2) operations. In many cases of practical importance only O(n log n) operations are required. An application to root-finding methods which use inverse interpolation is described, some results on multivariate power series are stated, and several open questions are mentioned.
Fast Matrix Multiplication With Applications
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Author : Jerzy S. Respondek
language : en
Publisher: Springer Nature
Release Date : 2025-02-26
Fast Matrix Multiplication With Applications written by Jerzy S. Respondek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-26 with Computers categories.
The ambition of this monograph is to show the methods of constructing fast matrix multiplication algorithms, and their applications, in an intelligible way, accessible not only to mathematicians. The scope and coverage of the book are comprehensive and constructive, and the analyses and algorithms can be readily applied by readers from various disciplines of science and technology who need modern tools and techniques related to fast matrix multiplication and related problems and techniques. Authors start from commutative algorithms, through exact non-commutative algorithms, partial algorithms to disjoint and arbitrary precision algorithms. Authors explain how to adapt disjoint algorithms to a single matrix multiplication and prove the famous tau-theorem in the (not so) special case. In an appendix, authors show how to work with confluent Vandermonde matrices, since they are used as an auxiliary tool in problems arising in fast matrix multiplication. Importantly, each algorithm is demonstrated by a concrete example of a decent dimensionality to ensure that all the mechanisms of the algorithms are illustrated. Finally, authors give a series of applications of fast matrix multiplication algorithms in linear algebra and other types of problems, including artificial intelligence.
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.
Modular Algorithms In Symbolic Summation And Symbolic Integration
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Author : Jürgen Gerhard
language : en
Publisher: Springer
Release Date : 2004-11-12
Modular Algorithms In Symbolic Summation And Symbolic Integration written by Jürgen Gerhard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-12 with Computers categories.
This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.
Computational Methods In Physics
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Author : Simon Širca
language : en
Publisher: Springer Nature
Release Date : 2025-04-01
Computational Methods In Physics written by Simon Širca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-01 with Science categories.
This textbook provides a compendium of numerical methods to assist physics students and researchers in their daily work. It carefully considers error estimates, stability and convergence issues, the choice of optimal methods, and techniques to increase program execution speeds. The book supplies numerous examples throughout the chapters that are concluded by more comprehensive problems with a strong physics background. Instead of uncritically employing modern black-box tools, the readers are encouraged to develop a more ponderous and skeptical approach. This revised and expanded edition now includes a new chapter on numerical integration and stable differentiation, as well as fresh material on optimal filtering, integration of gravitational many-body problems, computation of Poincaré maps, regularization of orbits, singular Sturm-Liouville problems, techniques for time evolution and spatial treatment of (semi)infinite domains in spectral methods, and phase retrieval. It also brings updated discussions of algebraic problems involving sparse matrices and of high-resolution schemes for partial differential equations.
The Parameterization Method For Invariant Manifolds
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Author : Àlex Haro
language : en
Publisher: Springer
Release Date : 2016-04-18
The Parameterization Method For Invariant Manifolds written by Àlex Haro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Mathematics categories.
This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.