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Eigenvalue Problem And Solution Pdf

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In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue and an associated eigenvector of a high-dimensional eigenvalue problem and prove some convergence results for these algorithms and their orthogonalized versions.

The properties of the eigenvalues and their corresponding eigenvectors are also discussed and used in solving questions. Free Mathematics Tutorials. About the author Download E-mail. In this example the eigenvalues are: a , e and g. Left multiply both sides of the above equation by matrix A.

Eigenvalues and eigenvectors

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Yiantsios and B. Yiantsios , B. Abstract An algorithm based on the compound matrix method is presented for solving difficult eigen-value problems. Details are given for systems of ordinary differential equations of fourth-order that are valid over connected domains coupled through interfacial conditions.

In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue and an associated eigenvector of a high-dimensional eigenvalue problem and prove some convergence results for these algorithms and their orthogonalized versions. The performance of our algorithms is illustrated on numerical test cases including the computation of the buckling modes of a microstructured plate and compared with that of another greedy algorithm for eigenvalue problems introduced by Ammar and Chinesta. This is a preview of subscription content, access via your institution. Rent this article via DeepDyve. Ammar, A. Fluid Mech. Baudouin, L.

Show all documents Designing Optical Fibers: Fitting the Derivatives of a Nonlinear Pde Eigenvalue Problem Solving the fiber optics problem was not a one way street of technology transfer and hopefully this paper will serve to highlight some of the linear algebraic advances that were stimulated by this application. Several non- linear eigensolvers that were applied to the problem were compared in [5], which in turn partly motivated the re- search in []. Each of these solvers required the solution of many symmetric indefinite tridiagonal sys- tems. Augmenting the simple model in 1 to handle a fiber wrapped around a spool, changed the tridiagonal eigenvalue problem to a 7-diagonal eigenvalue problem with the largest elements on the main diagonal and the outermost diagonal.

Greedy Algorithms for High-Dimensional Eigenvalue Problems

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Geometrically , an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. If T is a linear transformation from a vector space V over a field F into itself and v is a nonzero vector in V , then v is an eigenvector of T if T v is a scalar multiple of v. This can be written as. There is a direct correspondence between n -by- n square matrices and linear transformations from an n -dimensional vector space into itself, given any basis of the vector space.


Their solution leads to the problem of eigenvalues. Because of that, problem of eigenvalues occupies an important place in linear algebra.


Greedy Algorithms for High-Dimensional Eigenvalue Problems

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision Abstract: We present a method for solving systems of polynomial equations appearing in computer vision. We provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems PEPs and present a resultant-based method for transforming a system of polynomial equations to a polynomial eigenvalue problem.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Hwang and W.

Greedy Algorithms for High-Dimensional Eigenvalue Problems

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