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Author: Debajyoti Pal
Publisher:
ISBN:
Category :
Languages : en
Pages : 422
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Book Description
Triangular factorization, solution to linear equations, inversion, computation of rank profile and inertia (in the Hermitian case) etc. of general n x n matrices require O(n cubed) operations. For certain structured matrices including Toeplitz and Hankel matrices the computational complexity is known to be O(n squared) or better. These structured matrices often arise in a wide variety of areas including Signal processing. Systems theory and Communications. Fast (i.e. O(n squared)) algorithms for these structured matrices have been actively studied for over twenty five years. However almost all the authors have assumed that the underlying matrices are strongly regular i.e. every principal submatrix is nonsingular. Although some fast algorithms have recently been developed for certain problems involving some of these structured matrices which may have one or more zero minors, several other problems is lacking. In this dissertation, we obtain several new results through a unified approach to the problems mentioned earlier.
Author: Debajyoti Pal
Publisher:
ISBN:
Category :
Languages : en
Pages : 422
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Book Description
Triangular factorization, solution to linear equations, inversion, computation of rank profile and inertia (in the Hermitian case) etc. of general n x n matrices require O(n cubed) operations. For certain structured matrices including Toeplitz and Hankel matrices the computational complexity is known to be O(n squared) or better. These structured matrices often arise in a wide variety of areas including Signal processing. Systems theory and Communications. Fast (i.e. O(n squared)) algorithms for these structured matrices have been actively studied for over twenty five years. However almost all the authors have assumed that the underlying matrices are strongly regular i.e. every principal submatrix is nonsingular. Although some fast algorithms have recently been developed for certain problems involving some of these structured matrices which may have one or more zero minors, several other problems is lacking. In this dissertation, we obtain several new results through a unified approach to the problems mentioned earlier.
Author: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 0821831771
Category : Mathematics
Languages : en
Pages : 448
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Book Description
One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.
Author: T. Kailath
Publisher: SIAM
ISBN: 9781611971354
Category : Computers
Languages : en
Pages : 351
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Book Description
This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field. The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered. This book is not merely a collection of articles. The editors have gone to considerable lengths to blend the individual papers into a consistent presentation. Each chapter exposes the reader to some of the most recent research while providing enough background material to put the work into proper context.
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:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 302
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Book Description
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: 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: Michael K. Ng
Publisher: Numerical Mathematics and Scie
ISBN: 9780198504207
Category : Computers
Languages : en
Pages : 370
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Book Description
Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing.
Author: Vadim Olshevsky
Publisher: American Mathematical Soc.
ISBN: 9780821887585
Category : Mathematics
Languages : en
Pages : 452
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Book Description
One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.
Author:
Publisher:
ISBN:
Category : Electric circuits
Languages : en
Pages : 1170
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Book Description
