Structured Matrix Based Methods For Approximate Polynomial Gcd
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Structured Matrix Based Methods For Approximate Polynomial Gcd
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Author : Paola Boito
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-13
Structured Matrix Based Methods For Approximate Polynomial Gcd written by Paola Boito 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 2012-03-13 with Mathematics categories.
Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.
Advanced Numerical Methods In Applied Sciences
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Author : Luigi Brugnano
language : en
Publisher: MDPI
Release Date : 2019-06-20
Advanced Numerical Methods In Applied Sciences written by Luigi Brugnano and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with Juvenile Nonfiction categories.
The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
Computer Algebra In Scientific Computing
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Author : Vladimir P. Gerdt
language : en
Publisher: Springer
Release Date : 2013-08-15
Computer Algebra In Scientific Computing written by Vladimir P. Gerdt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Computers categories.
This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
Computer Algebra In Scientific Computing
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Author : François Boulier
language : en
Publisher: Springer Nature
Release Date : 2021-08-16
Computer Algebra In Scientific Computing written by François Boulier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-16 with Computers categories.
This book constitutes the proceedings of the 23rd International Workshop on Computer Algebra in Scientific Computing, CASC 2021, held in Sochi, Russia, in September 2021. The 24 full papers presented together with 1 invited talk were carefully reviewed and selected from 40 submissions. The papers cover theoretical computer algebra and its applications in scientific computing.
Numerical Methods For Structured Matrices And Applications
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Author : Dario Andrea Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-09
Numerical Methods For Structured Matrices And Applications written by Dario Andrea 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 2011-02-09 with Mathematics categories.
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.
Latent Variable Analysis And Signal Separation
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Author : Yannick Deville
language : en
Publisher: Springer
Release Date : 2018-06-05
Latent Variable Analysis And Signal Separation written by Yannick Deville and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Computers categories.
This book constitutes the proceedings of the 14th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2018, held in Guildford, UK, in July 2018.The 52 full papers were carefully reviewed and selected from 62 initial submissions. As research topics the papers encompass a wide range of general mixtures of latent variables models but also theories and tools drawn from a great variety of disciplines such as structured tensor decompositions and applications; matrix and tensor factorizations; ICA methods; nonlinear mixtures; audio data and methods; signal separation evaluation campaign; deep learning and data-driven methods; advances in phase retrieval and applications; sparsity-related methods; and biomedical data and methods.
Numerical Methods For Roots Of Polynomials Part Ii
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Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19
Numerical Methods For Roots Of Polynomials Part Ii written by J.M. McNamee and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.
The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average case inputs the resulting algorithms solve the polynomial factorization and root-finding problems within fixed sufficiently small error bounds by using nearly optimal arithmetic and Boolean time, that is using nearly optimal numbers of arithmetic and bitwise operations; in the case of a polynomial with integer coefficients and simple roots we can immediately extend factorization to root isolation, that is to computing disjoint covering discs, one for every root on the complex plane. The presented algorithms compute highly accurate approximations to all roots nearly as fast as one reads the input coefficients. Furthermore, our algorithms allow processor efficient parallel acceleration, which enables root-finding, factorization, and root isolation in polylogarithmic arithmetic and Boolean time. The chapter thoroughly covers the design and analysis of these algorithms, including auxiliary techniques of independent interest. At the end we compare the presented polynomial root-finders with alternative ones, in particular with the popular algorithms adopted by users based on supporting empirical information. We also comment on some promising directions to further progress.
Latin 2008 Theoretical Informatics
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Author : Eduardo Sany Laber
language : en
Publisher: Springer
Release Date : 2008-04-04
Latin 2008 Theoretical Informatics written by Eduardo Sany Laber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-04 with Computers categories.
This proceedings volume examines a range of topics in theoretical computer science, including automata theory, data compression, logic, machine learning, mathematical programming, parallel and distributed computing, quantum computing and random structures.
A Graduate Introduction To Numerical Methods
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Author : Robert M. Corless
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-12
A Graduate Introduction To Numerical Methods written by Robert M. Corless 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 2013-12-12 with Mathematics categories.
This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.
Structured Matrices And Polynomials
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Author : Victor Y. Pan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Structured Matrices And Polynomials written by Victor Y. Pan 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.
Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.