Matrices Moments And Quadrature With Applications

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Matrices, Moments and Quadrature with Applications

Gene H. Golub,Gérard Meurant
Matrices Moments and Quadrature with Applications Book PDF

Author : Gene H. Golub,Gérard Meurant
Publisher : Princeton University Press
Page : 376 pages
File Size : 55,6 Mb
Release : 2009-12-07
Category : Mathematics
ISBN : 9781400833887

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Matrices, Moments and Quadrature with Applications by Gene H. Golub,Gérard Meurant Pdf

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Matrix Completions, Moments, and Sums of Hermitian Squares

Mihály Bakonyi,Hugo J. Woerdeman
Matrix Completions Moments and Sums of Hermitian Squares Book PDF

Author : Mihály Bakonyi,Hugo J. Woerdeman
Publisher : Princeton University Press
Page : 533 pages
File Size : 51,6 Mb
Release : 2011-07-18
Category : Mathematics
ISBN : 9781400840595

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Matrix Completions, Moments, and Sums of Hermitian Squares by Mihály Bakonyi,Hugo J. Woerdeman Pdf

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.

Modern Discrete Mathematics and Analysis

Nicholas J. Daras,Themistocles M. Rassias
Modern Discrete Mathematics and Analysis Book PDF

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer
Page : 521 pages
File Size : 48,9 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319743257

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Modern Discrete Mathematics and Analysis by Nicholas J. Daras,Themistocles M. Rassias Pdf

A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.

Matrix Computations

Gene H. Golub,Charles F. Van Loan
Matrix Computations Book PDF

Author : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 781 pages
File Size : 41,5 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9781421408590

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Matrix Computations by Gene H. Golub,Charles F. Van Loan Pdf

A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

Error Norm Estimation in the Conjugate Gradient Algorithm

Gérard Meurant ,Petr Tichý
Error Norm Estimation in the Conjugate Gradient Algorithm Book PDF

Author : Gérard Meurant ,Petr Tichý
Publisher : SIAM
Page : 138 pages
File Size : 42,7 Mb
Release : 2024-01-30
Category : Mathematics
ISBN : 9781611977868

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Error Norm Estimation in the Conjugate Gradient Algorithm by Gérard Meurant ,Petr Tichý Pdf

The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.

Handbook in Monte Carlo Simulation

Paolo Brandimarte
Handbook in Monte Carlo Simulation Book PDF

Author : Paolo Brandimarte
Publisher : John Wiley & Sons
Page : 688 pages
File Size : 50,8 Mb
Release : 2014-06-20
Category : Business & Economics
ISBN : 9781118594513

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Handbook in Monte Carlo Simulation by Paolo Brandimarte Pdf

An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.

Mathematical Methods in Elasticity Imaging

Habib Ammari,Elie Bretin,Josselin Garnier,Hyeonbae Kang,Hyundae Lee,Abdul Wahab
Mathematical Methods in Elasticity Imaging Book PDF

Author : Habib Ammari,Elie Bretin,Josselin Garnier,Hyeonbae Kang,Hyundae Lee,Abdul Wahab
Publisher : Princeton University Press
Page : 239 pages
File Size : 54,9 Mb
Release : 2015-04-06
Category : Mathematics
ISBN : 9780691165318

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Mathematical Methods in Elasticity Imaging by Habib Ammari,Elie Bretin,Josselin Garnier,Hyeonbae Kang,Hyundae Lee,Abdul Wahab Pdf

This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

Modern Anti-windup Synthesis

Luca Zaccarian,Andrew R. Teel
Modern Anti windup Synthesis Book PDF

Author : Luca Zaccarian,Andrew R. Teel
Publisher : Princeton University Press
Page : 303 pages
File Size : 50,7 Mb
Release : 2011-07-11
Category : Mathematics
ISBN : 9781400839025

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Modern Anti-windup Synthesis by Luca Zaccarian,Andrew R. Teel Pdf

This book provides a wide variety of state-space--based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. Specifically, it addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem, the mathematical tools behind anti-windup algorithms, and more than twenty algorithms for anti-windup synthesis, illustrated with examples. Luca Zaccarian and Andrew Teel's modern method--combining a state-space approach with algorithms generated by solving linear matrix inequalities--treats MIMO and SISO systems with equal ease. The book, aimed at control engineers as well as graduate students, ranges from very simple anti-windup construction to sophisticated anti-windup algorithms for nonlinear systems. Describes the fundamental objectives and principles behind anti-windup synthesis for control systems with actuator saturation Takes a modern, state-space approach to synthesis that applies to both SISO and MIMO systems Presents algorithms as linear matrix inequalities that can be readily solved with widely available software Explains mathematical concepts that motivate synthesis algorithms Uses nonlinear performance curves to quantify performance relative to disturbances of varying magnitudes Includes anti-windup algorithms for a class of Euler-Lagrange nonlinear systems Traces the history of anti-windup research through an extensive annotated bibliography

Applied Linear Algebra in Action

Vasilios Katsikis
Applied Linear Algebra in Action Book PDF

Author : Vasilios Katsikis
Publisher : BoD – Books on Demand
Page : 175 pages
File Size : 42,5 Mb
Release : 2016-07-06
Category : Mathematics
ISBN : 9789535124191

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Applied Linear Algebra in Action by Vasilios Katsikis Pdf

The present text book contains a collection of six high-quality articles. In particular, this book is devoted to Linear Mathematics by presenting problems in Applied Linear Algebra of general or special interest.

High Performance Computing in Science and Engineering

Tomáš Kozubek,Martin Čermák,Petr Tichý,Radim Blaheta,Jakub Šístek,Dalibor Lukáš,Jiří Jaroš
High Performance Computing in Science and Engineering Book PDF

Author : Tomáš Kozubek,Martin Čermák,Petr Tichý,Radim Blaheta,Jakub Šístek,Dalibor Lukáš,Jiří Jaroš
Publisher : Springer
Page : 217 pages
File Size : 49,7 Mb
Release : 2018-07-16
Category : Computers
ISBN : 9783319971360

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High Performance Computing in Science and Engineering by Tomáš Kozubek,Martin Čermák,Petr Tichý,Radim Blaheta,Jakub Šístek,Dalibor Lukáš,Jiří Jaroš Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on High Performance Computing in Science and Engineering, HPCSE 2017, held in Karolinka, Czech Republic, in May 2017. The 15 papers presented in this volume were carefully reviewed and selected from 20 submissions. The conference provides an international forum for exchanging ideas among researchers involved in scientific and parallel computing, including theory and applications, as well as applied and computational mathematics. The focus of HPCSE 2017 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications.

Stability and Control of Large-Scale Dynamical Systems

Wassim M. Haddad,Sergey G. Nersesov
Stability and Control of Large Scale Dynamical Systems Book PDF

Author : Wassim M. Haddad,Sergey G. Nersesov
Publisher : Princeton University Press
Page : 389 pages
File Size : 41,8 Mb
Release : 2011-11-14
Category : Mathematics
ISBN : 9781400842667

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Stability and Control of Large-Scale Dynamical Systems by Wassim M. Haddad,Sergey G. Nersesov Pdf

Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

A Dynamical Systems Theory of Thermodynamics

Wassim M. Haddad
A Dynamical Systems Theory of Thermodynamics Book PDF

Author : Wassim M. Haddad
Publisher : Princeton University Press
Page : 744 pages
File Size : 45,9 Mb
Release : 2019-06-04
Category : Mathematics
ISBN : 9780691190143

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A Dynamical Systems Theory of Thermodynamics by Wassim M. Haddad Pdf

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach,I. G. Stratis,A. N. Yannacopoulos
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics Book PDF

Author : G. F. Roach,I. G. Stratis,A. N. Yannacopoulos
Publisher : Princeton University Press
Page : 399 pages
File Size : 55,9 Mb
Release : 2012-03-04
Category : Mathematics
ISBN : 9780691142173

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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics by G. F. Roach,I. G. Stratis,A. N. Yannacopoulos Pdf

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Topics in Quaternion Linear Algebra

Leiba Rodman
Topics in Quaternion Linear Algebra Book PDF

Author : Leiba Rodman
Publisher : Princeton University Press
Page : 379 pages
File Size : 50,5 Mb
Release : 2014-08-24
Category : Mathematics
ISBN : 9781400852741

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Topics in Quaternion Linear Algebra by Leiba Rodman Pdf

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Modern Methods in Scientific Computing and Applications

Anne Bourlioux,Martin Gander
Modern Methods in Scientific Computing and Applications Book PDF

Author : Anne Bourlioux,Martin Gander
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401005104

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Modern Methods in Scientific Computing and Applications by Anne Bourlioux,Martin Gander Pdf

When we first heard in the spring of 2000 that the Seminaire de matMmatiques superieures (SMS) was interested in devoting its session of the summer of 200l-its 40th-to scientific computing the idea of taking on the organizational work seemed to us somewhat remote. More immediate things were on our minds: one of us was about to go on leave to the Courant Institute, the other preparing for a research summer in Paris. But the more we learned about the possibilities of such a seminar, the support for the organization and also the great history of the SMS, the more we grew attached to the project. The topics we planned to cover were intended to span a wide range of theoretical and practical tools for solving problems in image processing, thin films, mathematical finance, electrical engineering, moving interfaces, and combustion. These applications alone show how wide the influence of scientific computing has become over the last two decades: almost any area of science and engineering is greatly influenced by simulations, and the SMS workshop in this field came very timely. We decided to organize the workshop in pairs of speakers for each of the eight topics we had chosen, and we invited the leading experts worldwide in these fields. We were very fortunate that every speaker we invited accepted to come, so the program could be realized as planned.