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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: 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: 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 The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.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: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 0821819216
Category : Matrices
Languages : en
Pages : 346
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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: 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:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Tom Lyche
Publisher: Springer Nature
ISBN: 3030364682
Category : Mathematics
Languages : en
Pages : 376
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Book Description
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Author: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 9780821856178
Category : Mathematics
Languages : en
Pages : 364
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Book Description
Many important problems in applied sciences, mathematics, and engineering can be reduced to matrix problems. Moreover, various applications often introduce a special structure into the corresponding matrices, so that their entries can be described by a certain compact formula. Classic examples include Toeplitz matrices, Hankel matrices, Vandermonde matrices, Cauchy matrices, Pick matrices, Bezoutians, controllability and observability matrices, and others. Exploiting these and the more general structures often allows us to obtain elegant solutions to mathematical problems as well as to design more efficient practical algorithms for a variety of applied engineering problems. Structured matrices have been under close study for a long time and in quite diverse (and seemingly unrelated) areas, for example, mathematics, computer science, and engineering. Considerable progress has recently been made in all these areas, and especially in studying the relevant numerical and computational issues. In the past few years, a number of practical algorithms blending speed and accuracy have been developed. This significant growth is fully reflected in these volumes, which collect 38 papers devoted to the numerous aspects of the topic. 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 numerical issues. The presentation fully illustrates the fact that the techniques of engineers, mathematicians, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices. The book is published in two volumes. The first contains articles on interpolation, system theory, signal and image processing, control theory, and spectral theory. Articles in the second volume are devoted to fast algorithms, numerical and iterative methods, and various applications.
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.
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: 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.