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Structured Matrices And Polynomials

Author: Victor Y. Pan
Publisher: Springer Science & Business Media
ISBN: 1461201292
Size: 39.68 MB
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This user-friendly, engaging textbook 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. The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.

Algorithms And Theory Of Computation Handbook Second Edition Volume 1

Author: Mikhail J. Atallah
Publisher: CRC Press
ISBN: 9781584888239
Size: 18.86 MB
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Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many of the existing chapters, this second edition contains four new chapters that cover external memory and parameterized algorithms as well as computational number theory and algorithmic coding theory. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics.

Numerical Methods For Structured Matrices And Applications

Author: Dario Andrea Bini
Publisher: Springer Science & Business Media
ISBN: 9783764389963
Size: 27.98 MB
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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.

Structured Matrix Based Methods For Approximate Polynomial Gcd

Author: Paola Boito
Publisher: Springer Science & Business Media
ISBN: 8876423818
Size: 43.43 MB
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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.

Matrix Computations And Semiseparable Matrices

Author: Raf Vandebril
Publisher: JHUP
ISBN: 9780801887147
Size: 64.49 MB
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In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

Hierarchische Matrizen

Author: Wolfgang Hackbusch
Publisher: Springer Science & Business Media
ISBN: 3642002218
Size: 27.96 MB
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Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. In dem Band stellt der Autor eine neuartige Methode dar, die es erstmals erlaubt, solche Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximativ durchzuführen. Anwendung findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.