Structure Preserving Doubling Algorithms For Nonlinear Matrix Equations
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Structure Preserving Doubling Algorithms For Nonlinear Matrix Equations
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Author : Tsung-Ming Huang
language : en
Publisher: SIAM
Release Date : 2018-10-04
Structure Preserving Doubling Algorithms For Nonlinear Matrix Equations written by Tsung-Ming Huang and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Mathematics categories.
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.
Solving Nonlinear Equations With Iterative Methods
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date :
Solving Nonlinear Equations With Iterative Methods written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Matrix Methods In Data Mining And Pattern Recognition Second Edition
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Author : Lars Elden
language : en
Publisher: SIAM
Release Date : 2019-08-30
Matrix Methods In Data Mining And Pattern Recognition Second Edition written by Lars Elden and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with Mathematics categories.
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.
Iterative Methods And Preconditioners For Systems Of Linear Equations
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Author : Gabriele Ciaramella
language : en
Publisher: SIAM
Release Date : 2022-02-08
Iterative Methods And Preconditioners For Systems Of Linear Equations written by Gabriele Ciaramella and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Mathematics categories.
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.
Riemann Problems And Jupyter Solutions
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Author : David I. Ketcheson
language : en
Publisher: SIAM
Release Date : 2020-06-26
Riemann Problems And Jupyter Solutions written by David I. Ketcheson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-26 with Mathematics categories.
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.
Location Estimation From The Ground Up
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Author : Sivan Toledo
language : en
Publisher: SIAM
Release Date : 2020-09-17
Location Estimation From The Ground Up written by Sivan Toledo and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-17 with Technology & Engineering categories.
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.
Computed Tomography
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Author : Per Christian Hansen
language : en
Publisher: SIAM
Release Date : 2021-09-25
Computed Tomography written by Per Christian Hansen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-25 with Mathematics categories.
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.
Fifth International Congress Of Chinese Mathematicians
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Fifth International Congress Of Chinese Mathematicians written by Lizhen Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.
Algorithms Of The Synthesis Of Optimal Regulations
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Author : F.A. ALIEV, V.B. LARIN, N.I. VELIEVA
language : en
Publisher: Outskirts Press
Release Date : 2022-03-30
Algorithms Of The Synthesis Of Optimal Regulations written by F.A. ALIEV, V.B. LARIN, N.I. VELIEVA and has been published by Outskirts Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-30 with Mathematics categories.
This book focuses on methods to solutions regarding matrix equations: algebraic, periodic, and unilateral Riccati equations, Lyapunov equations, Silvester equations, generalized Silvester equations, and factorization of matrix polynomials in continuous and discrete cases. These equations are used to solve problems of the synthesis of optimal controllers. Also presented is the problem of the synthesis of optimal controllers in the frequency domain when measuring part of the phase coordinates. A general parameterization algorithm is proposed for its solution. The well-known parameterizations (Youla–Jabr–Bongiorno (1976) and Desoer–Liu–Murrau–Saeks (1980)) are demonstrated by us to form a special case of the proposed general parameterization algorithm. The obtained results can be applied to solve various problems in oil production by the gas-lift method and rod pump systems, unmanned aerial vehicles, and walking machines. Each section is illustrated by examples. The MATLAB environment is used for numerical solution of the problems. The book is intended for students and experts in applied mathematics and control systems theory.
Matrix And Operator Equations And Applications
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Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2023-07-29
Matrix And Operator Equations And Applications written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.
This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.