Structured Matrices in Mathematics, Computer Science, and Engineering II
Structured Matrices in Mathematics, Computer Science, and Engineering II

Author: Vadim Olshevsky

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 362

ISBN-13: 0821820923

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"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.

Structured Matrices in Mathematics, Computer Science, and Engineering I
Structured Matrices in Mathematics, Computer Science, and Engineering I

Author: Vadim Olshevsky

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 346

ISBN-13: 0821819216

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"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.

Numerical Methods for Structured Matrices and Applications
Numerical Methods for Structured Matrices and Applications

Author: Dario Andrea Bini

Publisher: Springer Science & Business Media

Published: 2011-02-09

Total Pages: 439

ISBN-13: 3764389966

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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.

Fast Algorithms for Structured Matrices
Fast Algorithms for Structured Matrices

Author: Vadim Olshevsky

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 448

ISBN-13: 0821831771

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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.

Matrix Computations and Semiseparable Matrices
Matrix Computations and Semiseparable Matrices

Author: Raf Vandebril

Publisher: JHU Press

Published: 2008-11-12

Total Pages: 515

ISBN-13: 0801890527

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The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.

Separable Type Representations of Matrices and Fast Algorithms
Separable Type Representations of Matrices and Fast Algorithms

Author: Yuli Eidelman

Publisher: Springer Science & Business Media

Published: 2013-10-08

Total Pages: 404

ISBN-13: 303480606X

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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.​

Handbook of Linear Algebra
Handbook of Linear Algebra

Author: Leslie Hogben

Publisher: CRC Press

Published: 2013-11-26

Total Pages: 1906

ISBN-13: 1498785603

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With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering
Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering

Author: Edward L. Green

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 250

ISBN-13: 0821826794

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This volume presents the proceedings from the research conference, Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering, held at Mount Holyoke College, USA. It provides an overview of contemporary research in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop the theoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, noncommutative systems, and applications.

Theory and Computation of Tensors
Theory and Computation of Tensors

Author: Yimin Wei

Publisher: Academic Press

Published: 2016-08-28

Total Pages: 150

ISBN-13: 0128039809

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Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships. - Provides an introduction of recent results about tensors - Investigates theories and computations of tensors to broaden perspectives on matrices - Discusses how to extend numerical linear algebra to numerical multi-linear algebra - Offers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays