4 edition of The formulation and analysis of numerical methods for inverse eigenvalue problems. found in the catalog.
by Courant Institute of Mathematical Sciences, New York University in New York
Written in English
|The Physical Object|
|Number of Pages||55|
Methods for Computing Eigenvalues and Eigenvectors 10 De nition The characteristic polynomial of A, denoted P A (x) for x 2 R, is the degree n polynomial de ned by P A (x) = det(xI A): It is straightforward to see that the roots of the characteristic polynomial of a matrix are exactly the. Inverse problem. An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.
In fact, for the enormous size of eigenvalue problems, typically the size of the matrix is O(10^5~10^7), to calculate all the eigenvalues is an impossible job. If you want to solve it, implicitly QR methods for the standard eigenvalue problems and the QZ methods for generalized eigenvalue problems are . This text, based on the author's teaching at École Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods .
This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis. numerical methods for Civil Engineering majors during and was modi ed to include Mechanical Engineering in The materials have been periodically updated since then and underwent a major revision by the second author in The main goals of these lectures are to introduce concepts of numerical methods and introduce.
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We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem.
One of these methods is new. We study the case where multiple eigenvalues are given: we show how to state the problem so that it is not overdetermined, and describe how to modify the numerical methods to retain quadratic convergence on the modified by: Book Description. This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices.
For researchers in applied mathematics and scientific computing, and can also be used as a supplementary text for an advanced graduate course on these by: 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: The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems. We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem.
One of these methods is new. The purpose of this book is to describe recent developments in solving eigen- value problems, in particular with respect to the QR and QZ algorithms as well as structured matrices. Outline Mathematically speaking, the eigenvalues of a square matrix Aare the roots of its characteristic polynomial det(A I).
Numerical Methods for Inverse Eigenvalue Problems iii DECLARATION The author declares that the thesis represents his own work based on the ideas suggested by Prof. Raymond H. Chan, the author’s supervisor. All the work is done under the supervision of Prof. Raymond H. Chan during the period.
Spectral Schur complements. Nonlinear eigenvalue problems even arise from linear problems: A = A11 A 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.
Unitary Hessenberg inverse eigenvalue problems Inverse eigenvalue problems with prescribed entries Prescribed entries along the diagonal Prescribed entries at arbitrary locations Additive inverse eigenvalue problem revisit Cardinality and locations Numerical methods Inverse Singular value problems.
Numerical methods for large eigenvalue problems Danny C. Sorensen Department of Computational and Applied Mathematics, Rice University, Main St., MS, Houston, TXUSA E-mail: [email protected] Over the past decade considerable progress has been made towards the numer-File Size: KB.
() Convergence Analysis of Newton-Like Methods for Inverse Eigenvalue Problems with Multiple Eigenvalues. SIAM Journal on Numerical AnalysisAbstract | PDF ( KB)Cited by: Computing Eigenvalues and Eigenvectors 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 File Size: KB.
Matrix eigenvalue problems arise in a large number of disciplines of sciences and engineering. They constitute the basic tool used in designing buildings, bridges, and turbines, that are resistent to vibrations.
They allow to model queueing net- works, and to analyze stability of electrical networks File Size: 2MB. NONNEGATIVE INVERSE EIGENVALUE PROBLEMS H, ﬁnd a point in the intersection N i=1 C i (assuming the intersection is nonempty). (In fact, we will solely be interested in the case N = 2.) If all the C i’s in Problem are convex, a classical method of solving Problem is to alternatively project onto the C i’ method is often referred to as the.
This banner text can have markup. web; books; video; audio; software; images; Toggle navigationPages: Lecture 16 Numerical Methods for Eigenvalues As mentioned above, the eigenvalues and eigenvectors of an n nmatrix where n 4 must be found numerically instead of by hand. The numerical methods that are used in practice depend on the geometric meaning of eigenvalues and eigenvectors which is equation ().
The essence of all these methods isFile Size: KB. 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. Numerical Methods for Large Eigenvalue Problems This book was originally published by Manchester University Press (Oxford rd, Manchester, UK) in -- (ISBN 0 1) and in the US under Halstead Press (John Wiley, ISBN 0 7).
It is currently out of print. UNESCO – EOLSS SAMPLE CHAPTERS COMPUTATIONAL METHODS AND ALGORITHMS – Vol. I - Eigenvalue Problems: Methods of Eigenfunctions - V.I. Agoshkov and V.P. Shutyaev ©Encyclopedia of Life Support Systems (EOLSS) 1 r kk k uu cu∗ where u∗ is a particular solution and 12 ck rk, =, are arbitrary constants.
Eigenvalues and eigenfunctions often have clearly defined physical meaning: in the. Optimization problems involving eigenvalues arise in many different mathematical disciplines. This article is divided into two parts. Part I gives a historical account of the development of the field.
We discuss various applications that have been especially influential, from structural analysis to combinatorial optimization. Boundary Integral Equation Methods in Eigenvalue Problems of Elastodynamics and Thin Plates. Vol Pages () Formulation of Eigenvalue Problems by the Boundary Integral Equations.
Numerical Analysis of Eigenvalue Problems in .problems, linear programming problems in optimization, and some problems in dis-crete Fourier analysis.
There are a few problems in analysis or nonlinear problems that can be solved by analytical techniques, but the vast majority cannot. For such problems, the only way to obtain quantitative results is by using numerical methods to obtain File Size: 6MB.In Section 5 we present the numerical methods and results obtained for eigenvalues computation with spectral methods and nite ﬀ discretization, in in nite and bounded domain.
Comparison with theoretical results is done. Then in Section 6 we give conclusions and open problems. 2 A review of theoretical results obtained by functional analysis.