Inequality-Based Approximation of Matrix Eigenvectors

• Autorzy: Kocsor A. , Dombi J. , Balint I.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

eigenvectors; eigenvalues; inequalities; error bounds; iterative methods

PL

wektor własny; granice błędu; metoda iteracyjna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 4
• Strony: 533--538
• Opis fizyczny: Bibliogr. 10 poz., rys., tab.

Twórcy

autor

Kocsor A.

• Research Group on Artificial Intelligence, University of Szeged, Szeged, Hungary, H-6720, Aradi vrt. 1

autor

Dombi J.

• Department of Applied Informatics, University of Szeged, Szeged, Hungary, H-6720, Árpád tér 2

autor

Balint I.

• Department of Theoretical Physics, University of Szeged, Szeged, Hungary, H-6720, Tisza L. Krt. 84-86
• Department of Pharmaceutical Analysis, University of Szeged, Szeged, Hungary, H-6720, Somogyi u. 4
• Department of Natural Sciences, Dunaújváros Polytechnic, Dunaújváros, H-2400, Táncsics M. u. 1

Bibliografia

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• [2] Bellman R. (1970): Introduction to Matrix Analysis (2nd Ed.). - New York: McGraw-Hill.
• [3] Dragomir S.S. and Arslangić Š.Z. (1991): A refinement of the Cauchy-Buniakowski-Schwarz inequality for real numbers. - Radovi Matematičui (Sarajevo) Vol. 7, No. 2, pp. 299-303.
• [4] Eichhorn W. (1978): Functional Equations in Economics. - Reading, MA: Addison-Wesley.
• [5] Golub G.H. and Van Loan C.F. (1996): Matrix Computations (3rd Ed.). - Baltimore: The John Hopkins University Press.
• [6] Hardy G.H., Littlewood J.E. and Pólya G. (1934): Inequalities. - London: Cambridge University Press.
• [7] Kato T. (1966): Perturbation Theory of Linear Operators. - New York: Springer.
• [8] Mitrinović D.S., Pečarić and Fink J.E. (1993): Classical and New Inequalies in Analysis. - London: Kluwer.
• [9] Parlett B. (1980): The Symmetric Eigenvalue Problem. - Englewodd Cliffs: Prentice-Hall.
• [10] Wilkinson J.H. (1965): The Algebraic Eigenvalue Problem. - Oxford: Oxford University Press.