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Approximation And Bounds For Eigenvalues Of Various Domains Using The Intermediate Problem Technique
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Book Synopsis Approximation and Bounds for Eigenvalues of Various Domains Using the Intermediate Problem Technique by : Richard Edward Dame
Download or read book Approximation and Bounds for Eigenvalues of Various Domains Using the Intermediate Problem Technique written by Richard Edward Dame and published by . This book was released on 1972 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: A variational method was developed to obtain lower bounds for eigenvalues, eigenfunctions and general solutions to problems which have complicated boundary conditions or regional shapes. By using an intermediate-problem approach, field functions were expanded in a infinite Fourier type expansion in a Hilbert space of eigenfunctions of a conveniently related problem. Final solutions are developed by projecting the field function into a subspace which is orthogonal to a given infinite dimensional subspace of constraints. The purpose of the study is to develop a new method which could generate the difficult eigenfunctions and boundary-value problem solutions, since previous investigators have universally limited their developments of the intermediate problem method to eigenvalue determinations. The results of this study, therefore, show that solutions of difficult problems which were not accessible through other means can now be generated efficiently. (Author).
Book Synopsis Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications by : A. Weinstein
Download or read book Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications written by A. Weinstein and published by Elsevier. This book was released on 1972-06-23 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Variational Methods for Eigenvalue Problems by : S. H. Gould
Download or read book Variational Methods for Eigenvalue Problems written by S. H. Gould and published by University of Toronto Press. This book was released on 1966-12-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. From the reviews of this edition and from subsequent shorter expositions it has become clear that the method is of considerable interest to the mathematical world; this interest has increased greatly in recent years by the success of some mathematicians in simplifying and extending the numerical applications, particularly in quantum mechanics. Until now new developments have been available only in articles scattered throughout the literature: this second edition presents them systematically in the framework of the material contained in the first edition, which is retained in somewhat modified form.
Book Synopsis Variational Methods for Eigenvalue Approximation by : H. F. Weinberger
Download or read book Variational Methods for Eigenvalue Approximation written by H. F. Weinberger and published by SIAM. This book was released on 1974-01-01 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.
Book Synopsis Numerical Methods for Large Eigenvalue Problems by : Yousef Saad
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.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Upper and Lower Bounds for Eigenvalues by Finite Difference Methods by : Hans F. Weinberger
Download or read book Upper and Lower Bounds for Eigenvalues by Finite Difference Methods written by Hans F. Weinberger and published by . This book was released on 1955 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: A finite difference method is presented which gives a lower bound for the lowest eigenvalue of the membrane problem for any plane domain. Under certain assumptions on the domain one finds both upper and lower bounds for this eigenvalue by solving a single finite difference problem. The difference between the bounds can be estimated a priori and made arbitrarily small by choosing the mesh size sufficiently small.
Book Synopsis Bounds for Eigenvalues and the Method of Intermediate Problems by : A. Weinstein
Download or read book Bounds for Eigenvalues and the Method of Intermediate Problems written by A. Weinstein and published by . This book was released on 1960 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Collection of Technical Papers: Structures and materials by :
Download or read book A Collection of Technical Papers: Structures and materials written by and published by . This book was released on 1987 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Shock and Vibration Digest written by and published by . This book was released on 1972 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2006 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Bibliography by : Gerard De Vries
Download or read book Finite Element Bibliography written by Gerard De Vries and published by Springer. This book was released on 1976-12 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thjs bibliography had its inception in 1967, when the compilers first attempted a comprehensive cov erage of the finite element literature using both manual and computer-based retrieval. Initially, the data base was stored on a card index, but this was subsequently transferred to punched cards and magnetic tape. Computer processing was adopted at an early stage to derive the three index formats from the data base. Over the subsequent years, several versions of the bibliography were produced, with two of these being made available in a report form to other researchers. From the widespread interest in these documents, it became evident that there was a need for a commercially-available comprehensive bibliography in this area. A major effort was undertaken to revise, update, and extend the data base, resulting in this present volume. The bibliography covers the period 1956-1975 primarily, although some earlier publications of histori cal interest are included. The citations are not restricted to the English language and documents are listed in many languages and from diverse places of origin. All publication formats were accepted, so that references will be found to books, monographs, journal papers and articles, theses, dissertations, reports, surveys, and the like.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems by : Xuefeng Liu
Download or read book Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and published by Springer Nature. This book was released on with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Truncations in the Method of Intermediate Problems for Lower Bounds to Eigenvalues by : Norman W. Brazley
Download or read book Truncations in the Method of Intermediate Problems for Lower Bounds to Eigenvalues written by Norman W. Brazley and published by . This book was released on 1961 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper gives two new procedures for determining lower bounds to eigenvalues of semi-bounded self-adjoint operators. These procedures, while phrased in the language of Hilbert space, result in useful computational methods for the estimation of eigenvalues and eigenvectors of differential operators occurring in classical and quantum mechanics. Our procedures are based on the method of intermediate problems.
Book Synopsis Numerical Approximation of Partial Differential Equations by : Alfio Quarteroni
Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
Book Synopsis Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao
Download or read book Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
