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Core Chasing Algorithms For The Eigenvalue Problem
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Book Synopsis Core-Chasing Algorithms for the Eigenvalue Problem by : Jared L. Aurentz
Download or read book Core-Chasing Algorithms for the Eigenvalue Problem written by Jared L. Aurentz and published by SIAM. This book was released on 2018-07-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenvalue computations are ubiquitous in science and engineering. John Francis?s implicitly shifted QR algorithm has been the method of choice for small to medium sized eigenvalue problems since its invention in 1959. This book presents a new view of this classical algorithm. While Francis?s original procedure chases bulges, the new version chases core transformations, which allows the development of fast algorithms for eigenvalue problems with a variety of special structures. This also leads to a fast and backward stable algorithm for computing the roots of a polynomial by solving the companion matrix eigenvalue problem. The authors received a SIAM Outstanding Paper prize for this work. This book will be of interest to researchers in numerical linear algebra and their students.
Book Synopsis Inverse Eigenvalue Problems by : Moody Chu
Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by Oxford University Press. This book was released on 2005-06-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.
Book Synopsis Riemann Problems and Jupyter Solutions by : David I. Ketcheson
Download or read book Riemann Problems and Jupyter Solutions written by David I. Ketcheson and published by SIAM. This book was released on 2020-06-26 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. The solution of the Riemann problem captures essential information about these models and is the key ingredient in modern numerical methods for their solution. This book covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application. Riemann Problems and Jupyter Solutions is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations, allowing readers to grasp how the concepts presented are affected by important parameters and to experiment by varying those parameters themselves. The only interactive book focused entirely on the Riemann problem, it develops each concept in the context of a specific physical application, helping readers apply physical intuition in learning mathematical concepts. Graduate students and researchers working in the analysis and/or numerical solution of hyperbolic PDEs will find this book of interest. This includes mathematicians, as well as scientists and engineers, working on wave propagation problems. Educators interested in developing instructional materials using Jupyter notebooks will also find this book useful. The book is appropriate for courses in Numerical Methods for Hyperbolic PDEs and Analysis of Hyperbolic PDEs, and it can be a great supplement for courses in computational fluid dynamics, acoustics, and gas dynamics.
Book Synopsis Structured Matrices in Numerical Linear Algebra by : Dario Andrea Bini
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.
Book Synopsis Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations by : Tsung-Ming Huang
Download or read book Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations written by Tsung-Ming Huang and published by SIAM. This book was released on 2018-10-04 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear matrix equations arise frequently in applied science and engineering. This is the first book to provide a unified treatment of structure-preserving doubling algorithms that have been recently studied and proven effective for notoriously challenging problems, such as fluid queue theory and vibration analysis for high speed trains; present recent developments and results for the theory of doubling algorithms for nonlinear matrix equations associated with regular matrix pencils; and highlight the use of doubling algorithms in achieving robust solutions for notoriously challenging problems that other methods cannot. Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations is intended for researchers and computational scientists, and graduate students may also find it of interest.
Book Synopsis Numerical Methods for General and Structured Eigenvalue Problems by : Daniel Kressner
Download or read book Numerical Methods for General and Structured Eigenvalue Problems written by Daniel Kressner and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Book Synopsis Computed Tomography by : Per Christian Hansen
Download or read book Computed Tomography written by Per Christian Hansen and published by SIAM. This book was released on 2021-09-25 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes fundamental computational methods for image reconstruction in computed tomography (CT) with a focus on a pedagogical presentation of these methods and their underlying concepts. Insights into the advantages, limitations, and theoretical and computational aspects of the methods are included, giving a balanced presentation that allows readers to understand and implement CT reconstruction algorithms. Unique in its emphasis on the interplay between modeling, computing, and algorithm development, Computed Tomography: Algorithms, Insight, and Just Enough Theory develops the mathematical and computational aspects of three main classes of reconstruction methods: classical filtered back-projection, algebraic iterative methods, and variational methods based on nonlinear numerical optimization algorithms. It spotlights the link between CT and numerical methods, which is rarely discussed in current literature, and describes the effects of incomplete data using both microlocal analysis and singular value decomposition (SVD). This book sets the stage for further exploration of CT algorithms. Readers will be able to grasp the underlying mathematical models to motivate and derive the basic principles of CT reconstruction and will gain basic understanding of fundamental computational challenges of CT, such as the influence of noisy and incomplete data, as well as the reconstruction capabilities and the convergence of the iterative algorithms. Exercises using MATLAB are included, allowing readers to experiment with the algorithms and making the book suitable for teaching and self-study. Computed Tomography: Algorithms, Insight, and Just Enough Theory is primarily aimed at students, researchers, and practitioners interested in the computational aspects of X-ray CT and is also relevant for anyone working with other forms of tomography, such as neutron and electron tomography, that share the same mathematical formulation. With its basis in lecture notes developed for a PhD course, it is appropriate as a textbook for courses on computational methods for X-ray CT and computational methods for inverse problems.
Book Synopsis Solving Nonlinear Equations with Iterative Methods by : C. T. Kelley
Download or read book Solving Nonlinear Equations with Iterative Methods written by C. T. Kelley and published by SIAM. This book was released on with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This user-oriented guide describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others. A sequel to the author’s Solving Nonlinear Equations with Newton’s Methods (SIAM, 2003), this book contains new material on pseudo-transient continuation, mixed-precision solvers, and Anderson acceleration. It is supported by a Julia package and a suite of Jupyter notebooks and includes examples of nonlinear problems from many disciplines. This book is will be useful to researchers who solve nonlinear equations, students in numerical analysis, and the Julia community.
Book Synopsis Iterative Methods and Preconditioners for Systems of Linear Equations by : Gabriele Ciaramella
Download or read book Iterative Methods and Preconditioners for Systems of Linear Equations written by Gabriele Ciaramella and published by SIAM. This book was released on 2022-02-08 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.
Book Synopsis Location Estimation from the Ground Up by : Sivan Toledo
Download or read book Location Estimation from the Ground Up written by Sivan Toledo and published by SIAM. This book was released on 2020-09-17 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The location of an object can often be determined from indirect measurements using a process called estimation. This book explains the mathematical formulation of location-estimation problems and the statistical properties of these mathematical models. It also presents algorithms that are used to resolve these models to obtain location estimates, including the simplest linear models, nonlinear models (location estimation using satellite navigation systems and estimation of the signal arrival time from those satellites), dynamical systems (estimation of an entire path taken by a vehicle), and models with integer ambiguities (GPS location estimation that is centimeter-level accurate). Location Estimation from the Ground Up clearly presents analytic and algorithmic topics not covered in other books, including simple algorithms for Kalman filtering and smoothing, the solution of separable nonlinear optimization problems, estimation with integer ambiguities, and the implicit-function approach to estimating covariance matrices when the estimator is a minimizer or maximizer. It takes a unified approach to estimation while highlighting the differences between classes of estimation problems. The only book on estimation written for math and computer science students and graduates, it includes problems at the end of each chapter, many with solutions, to help readers deepen their understanding of the material and guide them through small programming projects that apply theory and algorithms to the solution of real-world location-estimation problems. The book’s core audience consists of engineers, including software engineers and algorithm developers, and graduate students who work on location-estimation projects and who need help translating the theory into algorithms, code, and deep understanding of the problem in front of them. Instructors in mathematics, computer science, and engineering may also find the book of interest as a primary or supplementary text for courses in location estimation and navigation.
Book Synopsis Matrix Methods in Data Mining and Pattern Recognition, Second Edition by : Lars Elden
Download or read book Matrix Methods in Data Mining and Pattern Recognition, Second Edition written by Lars Elden and published by SIAM. This book was released on 2019-08-30 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. This book is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.
Book Synopsis Numerical Analysis of Partial Differential Equations Using Maple and MATLAB by : Martin J. Gander
Download or read book Numerical Analysis of Partial Differential Equations Using Maple and MATLAB written by Martin J. Gander and published by SIAM. This book was released on 2018-01-01 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.
Book Synopsis Large Scale Eigenvalue Problems by : J. Cullum
Download or read book Large Scale Eigenvalue Problems written by J. Cullum and published by Elsevier. This book was released on 1986-01-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories: novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.
Book Synopsis Templates for the Solution of Algebraic Eigenvalue Problems by : Zhaojun Bai
Download or read book Templates for the Solution of Algebraic Eigenvalue Problems written by Zhaojun Bai and published by SIAM. This book was released on 2000-01-01 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.
Book Synopsis A Journey through the History of Numerical Linear Algebra by : Claude Brezinski
Download or read book A Journey through the History of Numerical Linear Algebra written by Claude Brezinski and published by SIAM. This book was released on 2022-12-06 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
Book Synopsis Modern Algorithms for Large Sparse Eigenvalue Problems by : Arnd Meyer
Download or read book Modern Algorithms for Large Sparse Eigenvalue Problems written by Arnd Meyer and published by Walter de Gruyter GmbH & Co KG. This book was released on 1987-12-31 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Modern Algorithms for Large Sparse Eigenvalue Problems".
Book Synopsis Algorithms for the Unitary Eigenvalue Problem by : Roden Jason A. David
Download or read book Algorithms for the Unitary Eigenvalue Problem written by Roden Jason A. David and published by . This book was released on 2007 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenvalues of unitary matrices arise in a variety of contexts in applied mathematics. This dissertation present four new algorithms for computing the eigenvalues of unitary matrices. In chapter 1, we give an overview these algorithms, and then survey the major applications where eigenvalues of unitary matrices arise. In chapter 2, we present the unitary QR algorithm, an algorithm that can used to compute all of the eigenvalues of a unitary matrix. In chapter 3, we present two Krylov space algorithms that approximate some of the eigenvalues of a large unitary matrix. Finally, in chapter 4, we present an algorithm that compute the eigenvalues of a unitary matrix U when U is expressed as a product U = U1...Un of unitary matrices of the same order. As a special case, we consider the generalized eigenvalue problem for unitary matrices.
