Author: Thomas J. Bella
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages :
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Book Description
Interplay between structured matrices and corresponding systems of polynomials is a classical topic, and two classical matrix classes, Jacobi (tridiagonal) matrices and unitary Hessenberg matrices that are often studied in this context are known to correspond to real orthogonal polynomials and Szegö polynomials, respectively. These two polynomial families arise in a wide variety of applications, and their short recurrence relations are often at the heart of a number of fast algorithms involving them. Historically, algorithms of this type have been developed first for real orthogonal polynomials, however, recently, several important algorithms originally derived for real orthogonal polynomials have subsequently been carried over to the class of Szegö polynomials. Such new algorithms tend to exploit the specific new structure, and thus are valid only for the Szegö polynomials; that is, they are analogues and not generalizations of the original algorithms. We present several results recently obtained for the â€superclass†of quasiseparable matrices, the latter class includes both Jacobi and unitary Hessenberg matrices. Hence the interplay between quasiseparable matrices and their polynomial systems (which contain both real orthogonal and Szegö polynomials) allows one to obtain true generalizations of several algorithms. Included herein are the Björck-Pereyra algorithm, the Traub algorithm, certain new digital filter structures, as well as QR and divide and conquer eigenvalue algorithms. Other results in structured matrices presented include a result on the possible effects of small, structure-preserving perturbations of a matrix self-adjoint with respect to an indefinite inner product on the so-called canonical Jordan bases of said matrix, and a result regarding Hadamard-Sylvester matrices in the theory of algebraic coding theory.
Author: Dario Andrea Bini
Publisher: Springer
ISBN: 3030040887
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.
Author: Michele Benzi
Publisher: Springer
ISBN: 3319498878
Category : Mathematics
Languages : en
Pages : 413
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Book Description
Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Author: Pavel G. Zhlobich
Publisher:
ISBN:
Category :
Languages : en
Pages : 672
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Book Description
Author: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 0821820923
Category : Mathematics
Languages : en
Pages : 362
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Book Description
"The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.
Author: Dario Andrea Bini
Publisher: Springer Science & Business Media
ISBN: 3764389966
Category : Mathematics
Languages : en
Pages : 439
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Book Description
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.
Author: Raf Vandebril
Publisher: JHU Press
ISBN: 0801896797
Category : Mathematics
Languages : en
Pages : 594
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Book Description
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.
Author: Victor Y. Pan
Publisher: Springer Science & Business Media
ISBN: 1461201292
Category : Mathematics
Languages : en
Pages : 299
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Book Description
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.
Author: Yuli Eidelman
Publisher: Springer Science & Business Media
ISBN: 303480606X
Category : Mathematics
Languages : en
Pages : 404
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Book Description
This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work is focused on algorithms of multiplication, inversion and description of eigenstructure and includes a large number of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part contains factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structure. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and the accessible style the text will be useful to engineers, scientists, numerical analysts, computer scientists and mathematicians alike.
Author: Dario Bini
Publisher: Nova Biomedical Books
ISBN:
Category : Mathematics
Languages : en
Pages : 222
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Book Description
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.
