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Saturday, August 8, 2020 | History

4 edition of Numerical methods for solving inverse eigenvalue problems. found in the catalog.

Numerical methods for solving inverse eigenvalue problems.

by Jorge Nocedal

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  • 15 Currently reading

Published by Courant Institute of Mathematical Sciences, New York University in New York .
Written in


Edition Notes

StatementBy Jorge Nocedal and Michael L. Overton.
ContributionsOverton, Michael L.
The Physical Object
Paginationv.p p.
ID Numbers
Open LibraryOL17980425M

T1 - FORMULATION AND ANALYSIS OF NUMERICAL METHODS FOR INVERSE EIGENVALUE PROBLEMS. AU - Friedland, S. AU - Nocedal, J. AU - Overton, M. L. PY - /1/1. Y1 - /1/1. N2 - We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue by: The Numerical Solution of Eigenvalue Problems By Theodore R. Goodman 1. Introduction. One method for solving eigenvalue problems on a digital computer is to convert the governing differential equations to finite difference equations, apply the boundary conditions at either end of the interval, and form a.

Inexact Numerical Methods for Inverse Eigenvalue Problems Zheng-jian Bai⁄ Novem Abstract In this paper, we survey some of the latest development in using inexact Newton-like methods for solving inverse eigenvalue problems. These methods require the solutions of nonsymmetric and large linear systems. One can solve the approximate Author: Zheng-jian Bai, 白正简. Overton, M, Friedland, S & Nocedal, J , Four quadratically convergent methods for solving inverse eigenvalue problems. in DF Griffiths (ed.), Numerical analysis. Pitman Research Notes in Mathematics Series , Wiley, New York, pp. Cited by: 6.

In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Keywords: polynomial eigenvalue problem, matrix polynomial, contour integral, projection method 1 Introduction The present paper is concerned with a numerical method to solve polynomial eigen-value problems. The polynomial eigenvalue problem (PEP) [1,4,7] involves finding an eigenvalue λ and corresponding nonzero eigenvector x that satisfy F.


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Numerical methods for solving inverse eigenvalue problems by Jorge Nocedal Download PDF EPUB FB2

Numerical experiments for additive, multiplicative and Toeplitz inverse eigenvalue problems are performed, showing rather satisfactory results.

Read more Article. 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 by: 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.

terns in dynamical systems. In fact the writing of this book was motivated mostly by the second class of problems.

Several books dealing with numerical methods for solving eigenvalue prob-lems involving symmetric (or Hermitian) matrices have been written and there are a few software packages both public and commercial available.

The bookFile Size: 2MB. SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () An inexact Cayley transform method for inverse eigenvalue problems with multiple by: () Numerical Methods for Solving Inverse Eigenvalue Problems for Nonnegative Matrices.

SIAM Journal on Matrix Analysis and ApplicationsAbstract | PDF ( KB)Cited by: T1 - NUMERICAL METHODS FOR SOLVING INVERSE EIGENVALUE PROBLEMS.

AU - Nocedal, Jorge. AU - Overton, Michael L. PY - /12/1. Y1 - /12/1. N2 - Additive inverse eigenvalue problem is discussed which arises in the solution of inverse Sturm-Liouville problems.

In practice it happens frequently that only some eigenvalues are by: Cite this paper as: Nocedal J., Overton M.L. () Numerical methods for solving inverse eigenvalue problems. In: Numerical Methods. Lecture Notes in Mathematics, vol Cited by: Lecture 16 Numerical Methods for Eigenvalues As mentioned above, the eigenvalues and eigenvectors of an n nmatrix where n 4 must be found Introduction to Numerical Methods by Young and Mohlenkamp c 63 Thus the v The following facts are at the heart of the Inverse Power Method: If is an eigenvalue of Athen 1= is an eigenvalue for File Size: KB.

Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields.

The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics. Exposition of numerical methods for solving inverse problem can be found, for instance, in [15, 16]. We can refer also to articles [17][18][19][20][21][22][23][24] devoted to different numerical.

Mathematical Modelling and Numerical Analysis M2AN, Vol. 33, No 5,p. { Mod elisation Math ematique et Analyse Num erique A NUMERICAL METHOD FOR SOLVING INVERSE EIGECited by: 2. The inverse power iteration computes the eigenvalue of smallest magnitude by computing the largest eigenvalue of the inverse.

Both the methods actually compute the eigenvector associated with the desired eigenvalue, and then the Rayleigh quotient finds the eigenvalue. this book is ideal for solving real-world problems.

Numerical Linear. Numerical methods vary in their behavior, and the many different types of differ-ential equation problems affect the performanceof numerical methods in a variety of ways.

An excellent book for “real world” examples of solving differential equations is that of Shampine, Gladwell, and Thompson [74].File Size: 1MB. ing certain symmetric inverse eigenvalue e eigenvalue problems have been of interest in many application areas, including particle physics and geology, as well as numerical integration methods based on Gaussian quadrature rules[14].

Examples of applications can be found in[ll], [12], [13], [24], [29]. Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions-the theoretic issue on solvability and the practical issue on computability.

Both questions are difficult and by: with numerical methods for solving eigenvalue problems, e.g., [39, 66, 22, 47, 62, 55, 32, 54].

Typically, eigensolvers are classi ed into methods for symmetric (or Hermitian) and nonsymmetric (or non-Hermitian) matrices, or methods for small, dense matrices and large, sparse matrices. This survey reviews popular methods for computing.

difference methods for initial value problems Download difference methods for initial value problems or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get difference methods for initial value problems book now.

This site is like a library, Use search box in the widget to get ebook that you want. Numerical Methods: Problems and Solutions By M.K.

Jain, S. Iyengar, R. Jain – Numerical Methods is an outline series containing brief text of numerical solution of transcendental and polynomial equations, system of linear algebraic equations and eigenvalue problems, interpolation and approximation, differentiation and integration, ordinary differential equations and complete.

( views) Numerical Methods for Large Eigenvalue Problems by Yousef Saad - SIAM, This book discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices.

It provides an in-depth view of the numerical methods for solving matrix eigenvalue problems that arise in various engineering applications. Numerical methods for ordinary differential equations. Numerical methods for ordinary differential equations — the numerical solution of ordinary differential equations (ODEs) Euler method — the most basic method for solving an ODE; Explicit and implicit methods — implicit methods need to solve an equation at every step.Inverse Power Iteration Observe that applying the power method to A 1 will nd the largest of 1 j, i.e., the smallest eigenvalue (by modulus).

If we have an eigenvalue estimate ˇ, then doing the power method for the matrix (A I) 1 will give the eigenvalue closest to. Convergence will be faster if is much closer to then to other Size: KB.Nonlinear eigenvalue problems even arise from linear problems: A = A11 A12 A21 A The spectral Schur complement is the inverse of a piece of the resolvent R(z) = (A zI) 1: S(z) = (R11(z)) 1 = A11 zI A12(A22 zI) 1A Can use to reduce a large linear eigenvalue problem to a smaller nonlinear eigenvalue problem.

Bounds on.