Numerical Solution of Eigenvalue Problems and Related Least Squares Problems

Project: Research project

Project Details

Description

This research seeks to improve the accuracy of methods to solve some particular eigenvalue problems. The first is the classical symmetric eigenvalue problem. Recent results have shown that there is a large class of symmetric eigenvalue problems for which small structured perturbations result in small changes in the eigenvalues in the relative sense. This class of matrices is called ``well-behaved''. The problem of finding a necessary and sufficient condition for a matrix to be ``well-behaved'' is being investigated. A number of related issues have to be considered, including: analysis of methods for updating indefinite eigenvalue problems; investigation of methods for updating the ULV and ULLV approximations to the singular value decomposition and generalized singular value decomposition; and development of analysis of methods for computing the sparse generalized singular value decomposition. The last two issues are extremely important in the solution of ill-posed least squares problems and total least squares problems. The implications of derived results for these problems are being investigated.

StatusFinished
Effective start/end date8/1/957/31/98

Funding

  • National Science Foundation: $149,627.00

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