Gersgorin-type eigenvalue inclusion theorems and their sharpness

Electronic Transactions on Numerical Analysis

Volumn 12, Issue , 2001, Pages 113-133

  Varga, Richard S ^a  

^a KENT STATE UNIVERSITY   (United States)

Author keywords

Brauer ovals of cassini; Brualdi lemniscate sets; Ger gorin disks; Minimal gers gorin sets

Indexed keywords

EID: 3042552171     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (8)

1. A. BRAVER, Limits for the characteristic roots of a matrix II, Duke Math. J. 14 (1947), pp. 21-26.
2. R. BRUALDI, Matrices, eigenvalues and directed graphs. Linear Multilinear Algebra 11 (1982), 143-165.
3. S. GERSCHGORIN, Über die Abgrenzung der Eigenwerte einer Matrix, Isv. Akad. Nauk USSR Ser. Mat., 7 (1931), pp. 749-754.
4. M. MARCUS AND H. MlNC, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston, 1964.
5. R. S. VARGA, Minimal Gerschgorin sets, Pacific J. Math., 15 (1965), pp. 719-729.
6. R. S. VARGA, Gerschgorin disks, Brauer ovals of Cassini (a vindication), and Bruatdi sets, Information (to appear).
7. R. S. VARGA AND A. KRAUTSTENGL, On Gersgorin-type problems and ovals of Cassini, Electron. Trans. Numer. Anal., 8 (1999), pp. 15-20.
8. J. L. WALSH, Interpolation and Approximation by Rational Functions in the Complex Domain, American Mathematical Society Colloquium Publication Volume XX, American Mathematical Society, 1965.