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Author : Shu-fang Xu
Publisher :
ISBN 13 : 9787301036020
Total Pages : 301 pages
Book Rating : 4.0/5 (36 download)
Download or read book An Introduction to Inverse Algebraic Eigenvalue Problems written by Shu-fang Xu and published by . This book was released on 1998 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Moody Chu
Publisher : Oxford University Press
ISBN 13 : 0198566646
Total Pages : 408 pages
Book Rating : 4.1/5 (985 download)
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.
Author : Shu-fang Xu
Publisher : Springer
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.3/5 (91 download)
Download or read book An Introduction to Inverse Algebraic Eigenvalue Problems written by Shu-fang Xu and published by Springer. This book was released on 1998 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraische Inverse Eigenwertprobleme behandeln die Frage, wie man die Elemente einer Matrix aus den Spektralwerten bestimmen kann. Dies ist ein zentrales Thema in vielen Problemkreisen (z. B. Kontrolltheorie, Molekularspektroskopie, Geologie).
Author : Fioralba Cakoni
Publisher : SIAM
ISBN 13 : 1611974453
Total Pages : 200 pages
Book Rating : 4.6/5 (119 download)
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2016-10-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance. Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues. The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.
Author : Moody Ten-Chao Chu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (12 download)
Download or read book Inverse Eigenvalue Problems written by Moody Ten-Chao Chu and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leslie Hogben
Publisher : American Mathematical Society
ISBN 13 : 1470466554
Total Pages : 302 pages
Book Rating : 4.4/5 (74 download)
Download or read book Inverse Problems and Zero Forcing for Graphs written by Leslie Hogben and published by American Mathematical Society. This book was released on 2022-07-21 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.
Author : S Friedland
Publisher : Legare Street Press
ISBN 13 : 9781021505194
Total Pages : 0 pages
Book Rating : 4.5/5 (51 download)
Download or read book The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems written by S Friedland and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse eigenvalue problems are among the most challenging and important topics in computational mathematics. This rigorous and accessible text offers a comprehensive introduction to the formulation and analysis of numerical methods for solving these problems, including a detailed discussion of the mathematical theory behind the methods and practical examples of their application. Whether you're a graduate student or an active researcher in the field, this book is an essential resource for mastering the latest techniques in inverse eigenvalue computation. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Graham M. L. Gladwell
Publisher : Springer Science & Business Media
ISBN 13 : 3709106966
Total Pages : 226 pages
Book Rating : 4.7/5 (91 download)
Download or read book Dynamical Inverse Problems: Theory and Application written by Graham M. L. Gladwell and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Author : Moody Ten-Chao Chu
Publisher :
ISBN 13 : 9780191718021
Total Pages : 387 pages
Book Rating : 4.7/5 (18 download)
Download or read book Inverse Eigenvalue Problems written by Moody Ten-Chao Chu and published by . This book was released on 2005 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the authors discuss the fundamental problems relating to Eigenvalue problems, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.
Author : Zhaojun Bai
Publisher : SIAM
ISBN 13 : 0898714710
Total Pages : 430 pages
Book Rating : 4.8/5 (987 download)
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 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : Steffen Börm
Publisher : Walter de Gruyter
ISBN 13 : 3110250373
Total Pages : 216 pages
Book Rating : 4.1/5 (12 download)
Download or read book Numerical Methods for Eigenvalue Problems written by Steffen Börm and published by Walter de Gruyter. This book was released on 2012-05-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenvalues and eigenvectors of matrices and linear operators play an important role when solving problems from structural mechanics and electrodynamics, e.g., by describing the resonance frequencies of systems, when investigating the long-term behavior of stochastic processes, e.g., by describing invariant probability measures, and as a tool for solving more general mathematical problems, e.g., by diagonalizing ordinary differential equations or systems from control theory. This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behavior with the goal to present an easily accessible introduction to the field, including rigorous proofs of all important results, but not a complete overview of the vast body of research. Several programming examples allow the reader to experience the behavior of the different algorithms first-hand. The book addresses students and lecturers of mathematics, physics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve new problems.
Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 9781611970739
Total Pages : 292 pages
Book Rating : 4.9/5 (77 download)
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Author : Fioralba Cakoni
Publisher : SIAM
ISBN 13 : 1611977428
Total Pages : 259 pages
Book Rating : 4.6/5 (119 download)
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2022-12-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
Author : Khosrow Chadan
Publisher : SIAM
ISBN 13 : 0898713870
Total Pages : 206 pages
Book Rating : 4.8/5 (987 download)
Download or read book An Introduction to Inverse Scattering and Inverse Spectral Problems written by Khosrow Chadan and published by SIAM. This book was released on 1997-01-01 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.
Author : G.M.L. Gladwell
Publisher : Springer Science & Business Media
ISBN 13 : 1402027214
Total Pages : 472 pages
Book Rating : 4.4/5 (2 download)
Download or read book Inverse Problems in Vibration written by G.M.L. Gladwell and published by Springer Science & Business Media. This book was released on 2006-01-14 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews
Author : Andreas Kirsch
Publisher : Springer Science & Business Media
ISBN 13 : 1441984747
Total Pages : 314 pages
Book Rating : 4.4/5 (419 download)
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Science & Business Media. This book was released on 2011-03-24 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.
Author : Per Christian Hansen
Publisher : SIAM
ISBN 13 : 089871883X
Total Pages : 220 pages
Book Rating : 4.8/5 (987 download)
Download or read book Discrete Inverse Problems written by Per Christian Hansen and published by SIAM. This book was released on 2010-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
