Spectral Approximation Of Linear Operators

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Spectral Approximation Of Linear Operators

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Author : Françoise Chaitin-Chatelin
language : en
Publisher:
Release Date : 1983

Spectral Approximation Of Linear Operators written by Françoise Chaitin-Chatelin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

The goal of this book is to be comprehensive, running the gamut from practical numerical results to a unifying framework of functional analysis, while simultaneously preserving the energy and excitement of presenting fresh research results. Its contents cover recent results, which either are scattered through the literature or appear here for the first time, as well as providing a nontraditional presentation of standard material.

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.

Spectral Approximation For Linear Operators And Applications

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Author :
language : en
Publisher:
Release Date : 2014

Spectral Approximation For Linear Operators And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

Linear Operator Equations Approximation And Regularization

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Author : M Thamban Nair
language : en
Publisher: World Scientific
Release Date : 2009-05-05

Linear Operator Equations Approximation And Regularization written by M Thamban Nair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-05 with Mathematics categories.

Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.

Perturbation Theory For Linear Operators

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Author : Tosio Kato
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Perturbation Theory For Linear Operators written by Tosio Kato 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 2013-06-29 with Mathematics categories.

Introduction To Spectral Theory

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Author : P.D. Hislop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Spectral Theory written by P.D. Hislop 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 Technology & Engineering categories.

The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.

Spectral Approximation Theory For Bounded Linear Operators

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Author : Wen-so Lo
language : en
Publisher:
Release Date : 1972

Spectral Approximation Theory For Bounded Linear Operators written by Wen-so Lo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Approximation theory categories.

In this thesis we examine the approximation theory of the eigenvalue problem of bounded linear operators defined on a Banach space, and its applications to integral and differential equations. Special cases include the degenerate kernel method, projection method, collocation method, the Galerkin method, the method of moments, and the generalized Ritz method for solving integral or differential equations. Given a bounded linear operator, a sequence of bounded linear operator approximations is assumed to converge to it in the operator norm. We examine, among other things, the perturbation of the spectrum of the given operator; criteria for the existence and convergence of approximate eigenvectors and generalized eigenvectors; relations between the dimensions of the eigenmanifolds and generalized eigenmanifolds of the operator and those of the approximate operators.

Advances In Underwater Acoustics Structural Acoustics And Computational Methodologies In 4 Volumes

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Author : Sean F Wu
language : en
Publisher: World Scientific
Release Date : 2025-04-29

Advances In Underwater Acoustics Structural Acoustics And Computational Methodologies In 4 Volumes written by Sean F Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-29 with Technology & Engineering categories.

This set of volumes encompasses the study of acoustics to diverse environments ranging from underwater and marine environments, to structural and civil engineering, computational models and aerospace engineering. Each volume comprises peer-reviewed publications in the related field of acoustics from the past decade, arranged such as to review the existing literature, examine new methodologies and then explore novel applications of pioneering acoustic principles. With contributions by eminent acoustics researchers, this set holds key insights for fellow acoustics researchers and engineers of any field impacted by acoustic phenomena.Volume 1's review chapters summarise theories like geoacoustic inversion as well as criticism of the Biot theory of propagation in fluid-saturated porous solids, while the new methodologies shown range from an efficient and stable coupled-mode solution to a cell-based smoothed radial point interpolation method. The book concludes with promising applications like experimental evidence of horizontal refraction and bottom attenuation coefficient inversion.Volume 2 reviews topics including radiation boundary conditions for the Helmholtz equation, and analytical interpretation of the early literature on the theory of vibrations. The methodologies range from coupled boundary element and energy flow method as well as sound radiation of a line source. The work concludes with promising applications like Lamb Waves in a poroelastic plate and experimental validations of reconstructed excitation forces acting inside a solid enclosure.Volume 3 provides summaries of theories including the benchmark study on eigenfrequencies of fluid-loaded structures, and the Burton and Miller method, while the new methodologies presented range from a coupled boundary element and energy flow method, to an efficient approach to the simulation of acoustic radiation. The volume concludes with promising applications like a comparison of transient infinite elements and transient Kirchhoff integral methods, as well as a fast multi-frequency iterative acoustic boundary element method.Volume 4 depicts the context of conventional methodologies including short-wave components and Galbrun's equation, while its new methodologies range from radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances to the effect of airfoil shape on trailing edge noise. The collection concludes with promising applications like helicopter noise predictions and conservative source interpolation methods for aeroacoustics.

Neural Approximations For Optimal Control And Decision

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Author : Riccardo Zoppoli
language : en
Publisher: Springer Nature
Release Date : 2019-12-17

Neural Approximations For Optimal Control And Decision written by Riccardo Zoppoli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-17 with Technology & Engineering categories.

Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: • a general functional optimization framework; • thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; • comparison of classical and neural-network based methods of approximate solution; • bounds to the errors of approximate solutions; • solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; • applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and • numerous, numerically detailed examples. The authors’ diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.

Eigenvalues Of Matrices

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Author : Francoise Chatelin
language : en
Publisher: SIAM
Release Date : 2013-01-03

Eigenvalues Of Matrices 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 2013-01-03 with Mathematics categories.

A comprehensive and accessible guide to the calculation of eigenvalues of matrices, ideal for undergraduates, or researchers/engineers in industry.