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Structured Matrices and Polynomials

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 292/5 ( reviews)

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Book Synopsis Structured Matrices and Polynomials by : Victor Y. Pan

Download or read book Structured Matrices and Polynomials written by Victor Y. Pan. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.

Structured Matrix Based Methods for Approximate Polynomial GCD

2012-03-13 Mathematics
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Release : 2012-03-13
Genre : Mathematics
Kind : eBook
Book Rating : 818/5 ( reviews)

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Book Synopsis Structured Matrix Based Methods for Approximate Polynomial GCD by : Paola Boito

Download or read book Structured Matrix Based Methods for Approximate Polynomial GCD written by Paola Boito. This book was released on 2012-03-13. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Polynomial and Matrix Computations

2012-12-06 Computers
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Release : 2012-12-06
Genre : Computers
Kind : eBook
Book Rating : 655/5 ( reviews)

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Book Synopsis Polynomial and Matrix Computations by : Dario Bini

Download or read book Polynomial and Matrix Computations written by Dario Bini. This book was released on 2012-12-06. 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.

On different concepts for the linearization of matrix polynomials and canonical decompositions of structured matrices with respect to indefinite sesquilinear forms

2019-05-30 Mathematics
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Release : 2019-05-30
Genre : Mathematics
Kind : eBook
Book Rating : 145/5 ( reviews)

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Book Synopsis On different concepts for the linearization of matrix polynomials and canonical decompositions of structured matrices with respect to indefinite sesquilinear forms by : Philip Saltenberger

Download or read book On different concepts for the linearization of matrix polynomials and canonical decompositions of structured matrices with respect to indefinite sesquilinear forms written by Philip Saltenberger. This book was released on 2019-05-30. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, a novel framework for the construction and analysis of strong linearizations for matrix polynomials is presented. Strong linearizations provide the standard means to transform polynomial eigenvalue problems into equivalent generalized eigenvalue problems while preserving the complete finite and infinite eigenstructure of the problem. After the transformation, the QZ algorithm or special methods appropriate for structured linearizations can be applied for finding the eigenvalues efficiently. The block Kronecker ansatz spaces proposed here establish an innovative and flexible approach for the construction of strong linearizations in the class of strong block minimal bases pencils. Moreover, they represent a new vector-space-setting for linearizations of matrix polynomials that additionally provides a common basis for various existing techniques on this task (such as Fiedler-linearizations). New insights on their relations, similarities and differences are revealed. The generalized eigenvalue problems obtained often allow for an efficient numerical solution. This is discussed with special attention to structured polynomial eigenvalue problems whose linearizations are structured as well. Structured generalized eigenvalue problems may also lead to equivalent structured (standard) eigenvalue problems. Thereby, the transformation produces matrices that can often be regarded as selfadjoint or skewadjoint with respect to some indefinite inner product. Based on this observation, normal matrices in indefinite inner product spaces and their spectral properties are studied and analyzed. Multiplicative and additive canonical decompositions respecting the matrix structure induced by the inner product are established.

Structured Matrices

2001 Mathematics
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Release : 2001
Genre : Mathematics
Kind : eBook
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Book Synopsis Structured Matrices by : Dario Bini

Download or read book Structured Matrices written by Dario Bini. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians from various countries assemble computational techniques that have developed and described over the past two decades to analyze matrices with structure, which are encountered in a wide variety of problems in pure and applied mathematics and in engineering. The 16 studies are on asymptotical spectral properties; algorithm design and analysis; issues specifically relating to structures, algebras, and polynomials; and image processing and differential equations. c. Book News Inc.

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