Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications
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Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications
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Author : A. Weinstein
language : en
Publisher: Elsevier
Release Date : 1972-06-23
Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications written by A. Weinstein and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-23 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications
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Author : Alexander Weinstein
language : en
Publisher:
Release Date : 1972
Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications written by Alexander Weinstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Calculus of variations categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank.
Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems
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Author : Xuefeng Liu
language : en
Publisher: Springer Nature
Release Date : 2024-06-25
Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-25 with Mathematics categories.
This monograph presents a study of newly developed guaranteed computational methodologies for eigenvalue problems of self-adjoint differential operators. It focuses on deriving explicit lower and upper bounds for eigenvalues, as well as explicit estimations for eigenfunction approximations. Such explicit error estimations rely on the finite element method (FEM) along with a new theory of explicit quantitative error estimation, diverging from traditional studies that primarily focus on qualitative results. To achieve quantitative error estimation, the monograph begins with an extensive analysis of the hypercircle method, that is, the Prager–Synge theorem. It introduces a novel a priori error estimation technique based on the hypercircle method. This facilitates the explicit estimation of Galerkin projection errors for equations such as Poisson's and Stokes', which are crucial for obtaining lower eigenvalue bounds via conforming FEMs. A thorough exploration of the fundamental theory of projection-based explicit lower eigenvalue bounds under a general setting of eigenvalue problems is also offered. This theory is extensively detailed when applied to model eigenvalue problems associated with the Laplace, biharmonic, Stokes, and Steklov differential operators, which are solved by either conforming or non-conforming FEMs. Moreover, there is a detailed discussion on the Lehmann–Goerisch theorem for the purpose of high-precision eigenvalue bounds, showing its relationship with previously established theorems, such as Lehmann–Maehly's method and Kato's bound. The implementation details of this theorem with FEMs, a topic rarely covered in existing literature, are also clarified. Lastly, the monograph introduces three new algorithms to estimate eigenfunction approximation errors, revealing the potency of classical theorems. Algorithm I extends Birkhoff’s result that works for simple eigenvalues to handle clustered eigenvalues, while Algorithm II generalizes the Davis–Kahan theorem, initially designed for strongly formulated eigenvalue problems, to address weakly formulated eigenvalue problems. Algorithm III utilizes the explicit Galerkin projection error estimation to efficiently handle Galerkin projection-based approximations.
Many Body Methods In Quantum Chemistry
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Author : Uzi Kaldor
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Many Body Methods In Quantum Chemistry written by Uzi Kaldor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The present volume contains the text of the invited lectures presented at the Symposium on Many Body Methods in Quantum Chemistry, held on the campus of Tel Aviv University in August 1988. The Symposium was a satellite meeting of the Sixth International Congress on Quantum Chemistry held in Jerusalem. The development and application of many-body methods in Quantum chemistry have been on the rise for a number of years. This is therefore a good time for an interim report on the state of the field. It is hoped that such a report is hereby provided, though it may not be complete. The Symposium was held under the auspices of Tel Aviv University, Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry. Other sponsors were the Israeli Academy of Sciences and Humanities, and the Israeli Ministry of Science and Development. Many thanks go to all of them. Finally, I would like to thank all the speakers and participants for making the meeting the enjoyable and (I hope) profitable experience it was. Tel Aviv, Israel Uzi Kaldor TESTS AND APPLICATIONS OF COMPLETE MODEL SPACE QUASIDEGENERATE MANY-BODY PERTURBATION THEORY FOR MOLECULES Karl F. Freed The James Franck Institute and Department of Chemistry The University of Chicago, Chicago, DUnois 60637 U.S.A.
Spectral Approximation Of Linear Operators
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Author : Francoise Chatelin
language : en
Publisher: SIAM
Release Date : 2011-05-26
Spectral Approximation Of Linear Operators written by Francoise Chatelin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.
Originally published: New York: Academic Press, 1983.
Vibrations And Waves In Continuous Mechanical Systems
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Author : Peter Hagedorn
language : en
Publisher: John Wiley & Sons
Release Date : 2007-10-22
Vibrations And Waves In Continuous Mechanical Systems written by Peter Hagedorn and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-22 with Science categories.
The subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems. The theory of vibrations in continuous systems is crucial to the understanding of engineering problems in areas as diverse as automotive brakes, overhead transmission lines, liquid filled tanks, ultrasonic testing or room acoustics. Starting from an elementary level, Vibrations and Waves in Continuous Mechanical Systems helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics. Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions. Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others. Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations. Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field. Includes exercises at the end of the chapters based on both the academic and practical experience of the authors. Vibrations and Waves in Continuous Mechanical Systems provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.
Numerical Methods For Large Eigenvalue Problems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2011-05-26
Numerical Methods For Large Eigenvalue Problems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.
This revised edition discusses numerical methods for computing the 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.
A Course In Mathematical Physics 3
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Author : Walter Thirring
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
A Course In Mathematical Physics 3 written by Walter Thirring and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
In this third volume of A Course in Mathematical Physics I have attempted not simply to introduce axioms and derive quantum mechanics from them, but also to progress to relevant applications. Reading the axiomatic litera ture often gives one the impression that it largely consists of making refined axioms, thereby freeing physics from any trace of down-to-earth residue and cutting it off from simpler ways of thinking. The goal pursued here, however, is to come up with concrete results that can be compared with experimental facts. Everything else should be regarded only as a side issue, and has been chosen for pragmatic reasons. It is precisely with this in mind that I feel it appropriate to draw upon the most modern mathematical methods. Only by their means can the logical fabric of quantum theory be woven with a smooth structure; in their absence, rough spots would . inevitably appear, especially in the theory of unbounded operators, where the details are too intricate to be comprehended easily. Great care has been taken to build up this mathematical weaponry as completely as possible, as it is also the basic arsenal of the next volume. This means that many proofs have been tucked away in the exercises. My greatest concern was to replace the ordinary cal culations of uncertain accuracy with better ones having error bounds, in order to raise the crude manners of theoretical physics to the more cultivated level of experimental physics.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1969
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mechanics, Applied categories.
Bounds For Eigenvalues And The Method Of Intermediate Problems
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Author : A. Weinstein
language : en
Publisher:
Release Date : 1960
Bounds For Eigenvalues And The Method Of Intermediate Problems written by A. Weinstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Eigenvalues categories.