# Inequality-based approximation of matrix eigenvectors

András Kocsor; József Dombi; Imre Bálint

International Journal of Applied Mathematics and Computer Science (2002)

- Volume: 12, Issue: 4, page 533-538
- ISSN: 1641-876X

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topKocsor, András, Dombi, József, and Bálint, Imre. "Inequality-based approximation of matrix eigenvectors." International Journal of Applied Mathematics and Computer Science 12.4 (2002): 533-538. <http://eudml.org/doc/207608>.

@article{Kocsor2002,

abstract = {A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.},

author = {Kocsor, András, Dombi, József, Bálint, Imre},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {error bounds; eigenvalues; eigenvectors; inequalities; iterative methods; non-negative functions; global minima; optimization},

language = {eng},

number = {4},

pages = {533-538},

title = {Inequality-based approximation of matrix eigenvectors},

url = {http://eudml.org/doc/207608},

volume = {12},

year = {2002},

}

TY - JOUR

AU - Kocsor, András

AU - Dombi, József

AU - Bálint, Imre

TI - Inequality-based approximation of matrix eigenvectors

JO - International Journal of Applied Mathematics and Computer Science

PY - 2002

VL - 12

IS - 4

SP - 533

EP - 538

AB - A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.

LA - eng

KW - error bounds; eigenvalues; eigenvectors; inequalities; iterative methods; non-negative functions; global minima; optimization

UR - http://eudml.org/doc/207608

ER -

## References

top- Bazaraa M.S. , Sherali H.D. and Shetty C.M. (1993): Nonlinear Programming Theory and Algorithms. - New York: Wiley. Zbl0774.90075
- Bellman R. (1970): Introduction to Matrix Analysis (2nd Ed.). - New York: McGraw-Hill. Zbl0216.06101
- Dragomir S.S. and Arslangic uS.Z. (1991): A refinement of the Cauchy-Buniakowski-Schwarz inequality for real numbers. - Radovi Matematičui (Sarajevo) Vol. 7, No. 2, pp. 299-303. Zbl0748.26010
- Eichhorn W. (1978): Functional Equations in Economics. -Reading, MA: Addison-Wesley. Zbl0397.90002
- Golub G.H. and Van Loan C.F. (1996): Matrix Computations (3rd Ed.). - Baltimore: The John Hopkins University Press. Zbl0865.65009
- Hardy G.H., Littlewood J.E. and Pólya G. (1934): Inequalities. - London: Cambridge University Press.
- Kato T. (1966): Perturbation Theory of Linear Operators. - New York: Springer. Zbl0148.12601
- Mitrinovic D.S., Pečaric and Fink J.E.(1993): Classical and New Inequalities in Analysis. - London: Kluwer. Zbl0771.26009
- Parlett B. (1980): The Symmetric Eigenvalue Problem. - Englewodd Cliffs: Prentice-Hall. Zbl0431.65017
- Wilkinson J.H. (1965): The Algebraic Eigenvalue Problem. - Oxford: Oxford University Press. Zbl0258.65037

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