Download or read book Topics in Numerical Linear Algebra Related to Quasiseparable and Other Structured Matrices written by Thomas J. Bella and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Structured Matrices in Numerical Linear Algebra written by Dario Andrea Bini and published by Springer. This book was released on 2019-04-08 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Exploiting Hidden Structure in Matrix Computations Algorithms and Applications written by Michele Benzi and published by Springer. This book was released on 2017-01-24 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quasiseparable Matrices and Polynomials written by Pavel G. Zhlobich and published by . This book was released on 2011 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structured Matrices in Mathematics Computer Science and Engineering II written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on 2001 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Numerical Methods for Structured Matrices and Applications written by Dario Andrea Bini and published by Springer Science & Business Media. This book was released on 2011-02-09 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2008-01-14 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Structured Matrices and Polynomials written by Victor Y. Pan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. 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.
Download or read book Separable Type Representations of Matrices and Fast Algorithms written by Yuli Eidelman and published by Springer Science & Business Media. This book was released on 2013-10-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Structured Matrices written by Dario Bini and published by Nova Biomedical Books. This book was released on 2001 with total page 222 pages. 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.
Download or read book Computational Matrix Analysis written by Alan J. Laub and published by SIAM. This book was released on 2012-01-01 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition estimation in book form for the first time; and an overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic; discussion and examples of conditioning, stability, and rounding analysis; an introduction to mathematical software topics related to numerical linear algebra; a thorough introduction to Gaussian elimination, along with condition estimation techniques; coverage of linear least squares, with orthogonal reduction and QR factorization; variants of the QR algorithm; and applications of the discussed algorithms.
Download or read book Numerical Algebra Matrix Theory Differential Algebraic Equations and Control Theory written by Peter Benner and published by Springer. This book was released on 2015-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Download or read book Special Issue Structured Matrices with Applications written by Raymond Chan and published by . This book was released on 2005 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Matrix Analysis written by Ilse C. F. Ipsen and published by SIAM. This book was released on 2009-01-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to promote understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. Sensitivity and stability are analyzed as mathematical properties, without reference to finite precision arithmetic. The material is presented at a basic level, emphasizing ideas and intuition, but in a mathematically rigorous fashion. The derivations are simple and elegant, and the results are easy to understand and interpret. The book is self-contained. It was written for students in all areas of mathematics, engineering, and the computational sciences, but can easily be used for self-study. This text differs from other numerical linear algebra texts by offering the following: a systematic development of numerical conditioning; a simplified concept of numerical stability in exact arithmetic; simple derivations; a high-level view of algorithms; and results for complex matrices.
Download or read book Nonnegative Matrices and Applicable Topics in Linear Algebra written by Alexander Graham and published by Dover Publications. This book was released on 2019-11-13 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonnegative matrices is an increasingly important subject in economics, control theory, numerical analysis, Markov chains, and other areas. This concise treatment is directed toward undergraduates who lack specialized knowledge at the postgraduate level of mathematics and related fields, such as mathematical economics and operations research. An Introductory Survey encompasses some aspects of matrix theory and its applications and other relevant topics in linear algebra, including certain facets of graph theory. Subsequent chapters cover various points of the theory of normal matrices, comprising unitary and Hermitian matrices, and the properties of positive definite matrices. An exploration of the main topic, nonnegative matrices, is followed by a discussion of M-matrices. The final chapter examines stochastic, genetic, and economic models. The important concepts are illustrated by simple worked examples. Problems appear at the conclusion of most chapters, with solutions at the end of the book.
Download or read book Matrices written by Shmuel Friedland and published by World Scientific. This book was released on 2015-10-29 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics."--
Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2008-12-15 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
