The J Matrix Method

Author : Abdulaziz D. Alhaidari,Eric J. Heller,Hashim A. Yamani,Mohamed S. Abdelmonem
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 53,9 Mb
Release : 2008-03-20
Category : Science
ISBN : 9781402060731

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The J-Matrix Method by Abdulaziz D. Alhaidari,Eric J. Heller,Hashim A. Yamani,Mohamed S. Abdelmonem Pdf

Although introduced30 years ago, the J-matrix method has witnessed a resurgence of interest in the last few years. In fact, the interest never ceased, as some authors have found in this method an effective way of handling the continuous spectrum of scattering operators, in addition to other operators. The motivation behind the introduction of the J-matrix method will be presented in brief. The introduction of fast computing machines enabled theorists to perform cal- lations, although approximate, in a conveniently short period of time. This made it possible to study varied scenarios and models, and the effects that different possible parameters have on the ?nal results of such calculations. The ?rst area of research that bene?ted from this opportunity was the structural calculation of atomic and nuclear systems. The Hamiltonian element of the system was set up as a matrix in a convenient, ?nite, bound-state-like basis. A matrix of larger size resulted in a better con?guration interaction matrix that was subsequently diagonalized. The discrete energy eigenvalues thus obtained approximated the spectrum of the system, while the eigenfunctions approximated the wave function of the resulting discrete state. Structural theorists were delighted because they were able to obtain very accurate values for the lowest energy states of interest.

Author : John J. Uicker,Pradip N. Sheth,Bahram Ravani
Publisher : Cambridge University Press
Page : 347 pages
File Size : 41,8 Mb
Release : 2013-04-15
Category : Computers
ISBN : 9780521761093

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Matrix Methods in the Design Analysis of Mechanisms and Multibody Systems by John J. Uicker,Pradip N. Sheth,Bahram Ravani Pdf

This is an integrated approach to kinematic and dynamic analysis. The matrix techniques presented are general and applicable to two- or three-dimensional systems. The techniques lend themselves to programming and digital computation and can be a usable tool for designers, and are applicable to the design analysis of all multibody mechanical systems.

Author : Vadim Olshevsky
Publisher : World Scientific
Page : 604 pages
File Size : 46,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812836014

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Matrix Methods by Vadim Olshevsky Pdf

Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume. --

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814469555

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Matrix Methods: Theory, Algorithms and Applications by Anonim Pdf

Author : Xiaoting Rui,Guoping Wang,Jianshu Zhang
Publisher : John Wiley & Sons
Page : 768 pages
File Size : 43,7 Mb
Release : 2018-10-01
Category : Mathematics
ISBN : 9781118724828

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Transfer Matrix Method for Multibody Systems by Xiaoting Rui,Guoping Wang,Jianshu Zhang Pdf

TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS Xiaoting Rui, Guoping Wang and Jianshu Zhang - Nanjing University of Science and Technology, China Featuring a new method of multibody system dynamics, this book introduces the transfer matrix method systematically for the first time. First developed by the lead author and his research team, this method has found numerous engineering and technological applications. Readers are first introduced to fundamental concepts like the body dynamics equation, augmented operator and augmented eigenvector before going in depth into precision analysis and computations of eigenvalue problems as well as dynamic responses. The book also covers a combination of mixed methods and practical applications in multiple rocket launch systems, self-propelled artillery as well as launch dynamics of on-ship weaponry. • Comprehensively introduces a new method of analyzing multibody dynamics for engineers • Provides a logical development of the transfer matrix method as applied to the dynamics of multibody systems that consist of interconnected bodies • Features varied applications in weaponry, aeronautics, astronautics, vehicles and robotics Written by an internationally renowned author and research team with many years' experience in multibody systems Transfer Matrix Method of Multibody System and Its Applications is an advanced level text for researchers and engineers in mechanical system dynamics. It is a comprehensive reference for advanced students and researchers in the related fields of aerospace, vehicle, robotics and weaponry engineering.

Author : Richard Bronson,Gabriel B. Costa
Publisher : Academic Press
Page : 432 pages
File Size : 44,8 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 0080922252

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Matrix Methods by Richard Bronson,Gabriel B. Costa Pdf

Matrix Methods: Applied Linear Algebra, Third Edition, as a textbook, provides a unique and comprehensive balance between the theory and computation of matrices. The application of matrices is not just for mathematicians. The use by other disciplines has grown dramatically over the years in response to the rapid changes in technology. Matrix methods is the essence of linear algebra and is what is used to help physical scientists; chemists, physicists, engineers, statisticians, and economists solve real world problems. Applications like Markov chains, graph theory and Leontief Models are placed in early chapters Readability- The prerequisite for most of the material is a firm understanding of algebra New chapters on Linear Programming and Markov Chains Appendix referencing the use of technology, with special emphasis on computer algebra systems (CAS) MATLAB

Author : R. K. Livesley
Publisher : Elsevier
Page : 281 pages
File Size : 51,6 Mb
Release : 2014-05-16
Category : Technology & Engineering
ISBN : 9781483136264

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Matrix Methods of Structural Analysis by R. K. Livesley Pdf

Matrix Methods of Structural Analysis presents how concepts and notations of matrix algebra can be applied to arriving at general systematic approach to structure analysis. The book describes the use of matrix notation in structural analysis as being theoretically both compact and precise, but also, quite general. The text also presents, from the practical point of view, matrix notation as providing a systematic approach to the analysis of structures related to computer programming. Matrix algebraic methods are useful in repeated calculations where manual work becomes tedious. The Gaus-Seidel method and linear programming are two methods to use in solving simultaneous equations. The book then describes the notation for loads and displacements, on sign conventions, stiffness and flexibility matrices, and equilibrium and compatibility conditions. The text discusses the formulation of the equilibrium method using connection matrices and an alternative method. The book evaluates the compatibility method as programmed in a computer; and it discusses the analysis of a pin-jointed truss and of a rigid-jointed truss. The book presents some problems when using computers for analyzing structures, such as decision strategy, accuracy, and checks conducted on handling large matrices. The text also analyzes structures that behave in a non-linear manner. The book is suitable for structural engineers, physicist, civil engineers, and students of architectural design.

Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 44,8 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783319050898

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Numerical Methods in Matrix Computations by Åke Björck Pdf

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Author : Timothy G. Feeman
Publisher : Springer Nature
Page : 330 pages
File Size : 50,9 Mb
Release : 2023-11-24
Category : Mathematics
ISBN : 9783031395628

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Applied Linear Algebra and Matrix Methods by Timothy G. Feeman Pdf

This textbook is designed for a first course in linear algebra for undergraduate students from a wide range of quantitative and data driven fields. By focusing on applications and implementation, students will be prepared to go on to apply the power of linear algebra in their own discipline. With an ever-increasing need to understand and solve real problems, this text aims to provide a growing and diverse group of students with an applied linear algebra toolkit they can use to successfully grapple with the complex world and the challenging problems that lie ahead. Applications such as least squares problems, information retrieval, linear regression, Markov processes, finding connections in networks, and more, are introduced on a small scale as early as possible and then explored in more generality as projects. Additionally, the book draws on the geometry of vectors and matrices as the basis for the mathematics, with the concept of orthogonality taking center stage. Important matrix factorizations as well as the concepts of eigenvalues and eigenvectors emerge organically from the interplay between matrix computations and geometry. The R files are extra and freely available. They include basic code and templates for many of the in-text examples, most of the projects, and solutions to selected exercises. As much as possible, data sets and matrix entries are included in the files, thus reducing the amount of manual data entry required.

Author : Charles W Swartz
Publisher : World Scientific
Page : 222 pages
File Size : 51,8 Mb
Release : 1996-08-22
Category : Mathematics
ISBN : 9789814498715

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Infinite Matrices And The Gliding Hump, Matrix Methods In Analysis by Charles W Swartz Pdf

These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.

Author : Lars Elden
Publisher : SIAM
Page : 226 pages
File Size : 54,7 Mb
Release : 2007-07-12
Category : Computers
ISBN : 9780898716269

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Matrix Methods in Data Mining and Pattern Recognition by Lars Elden Pdf

Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.

Author : Piotr Antosik,Charles Swartz
Publisher : Springer
Page : 118 pages
File Size : 42,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540392668

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Matrix Methods in Analysis by Piotr Antosik,Charles Swartz Pdf

Author : Judith Garrard
Publisher : Jones & Bartlett Learning
Page : 225 pages
File Size : 53,6 Mb
Release : 2011
Category : Language Arts & Disciplines
ISBN : 9780763771867

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Health Sciences Literature Review Made Easy by Judith Garrard Pdf

Health Sciences Literature Review Made Easy helps students and practitioners better understand scientific literature by instilling the essential skills (via the matrix method) needed to critically evaluate article findings. the fundamental principles of searching, organizing, reviewing, and synthesizing are covered at the most basic level. Visual examples and a single case study are woven throughout the text. This easy-to-read and practical reference is an invaluable aid to students, researchers, and practitioners. the Third Edition has been completely revised and updated to reflect the switch

Author : Romain Couillet,Zhenyu Liao
Publisher : Cambridge University Press
Page : 412 pages
File Size : 53,8 Mb
Release : 2022-07-21
Category : Computers
ISBN : 9781009301893

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Random Matrix Methods for Machine Learning by Romain Couillet,Zhenyu Liao Pdf

This book presents a unified theory of random matrices for applications in machine learning, offering a large-dimensional data vision that exploits concentration and universality phenomena. This enables a precise understanding, and possible improvements, of the core mechanisms at play in real-world machine learning algorithms. The book opens with a thorough introduction to the theoretical basics of random matrices, which serves as a support to a wide scope of applications ranging from SVMs, through semi-supervised learning, unsupervised spectral clustering, and graph methods, to neural networks and deep learning. For each application, the authors discuss small- versus large-dimensional intuitions of the problem, followed by a systematic random matrix analysis of the resulting performance and possible improvements. All concepts, applications, and variations are illustrated numerically on synthetic as well as real-world data, with MATLAB and Python code provided on the accompanying website.

Author : Romain Couillet,Mérouane Debbah
Publisher : Cambridge University Press
Page : 562 pages
File Size : 44,9 Mb
Release : 2011-09-29
Category : Technology & Engineering
ISBN : 9781139504966

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Random Matrix Methods for Wireless Communications by Romain Couillet,Mérouane Debbah Pdf

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.