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The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems
Abstract
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 problem. We give a general convergence analysis, which covers both the distinct and the multiple eigenvalue cases. We also present numerical experiments which illustrate our results.
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Citations
Cited by
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
Alizadeh, F. (1995) · SIAM Journal on Optimization · doi:10.1137/0805002 · Cited by 892
A survey of matrix inverse eigenvalue problems
Boley, D., & Golub, G. H. (1987) · Inverse Problems · doi:10.1088/0266-5611/3/4/010 · Cited by 223
Metadata
- Authors
- Friedland, S., Nocedal, J., & Overton, M. L.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1987-06
- Volume
- 24
- Issue
- 3
- Pages
- 634-667
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W4294571370
- Cited by
- 163
- References
- 0
- FWCI
- 2.83
- Type
- journal article
- Language
- en
- Open access
- closed
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- Friedland, S., Nocedal, J., & Overton, M. L. (1987). The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0724043
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