Nested bounds for the spectral radius
Article
Received:
- 46 Downloads
- 12 Citations
Keywords
Mathematical Method Spectral Radius Nest Bound
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Bohl, E.: Eigenwertaufgaben bei monotonen Operatoren und Fehlerabschätzungen für Operatorgleichungen. Arch. Rational Mech. Anal.22, 313–332 (1966).Google Scholar
- 2.Collatz, L.: Einschließungssätze für die Eigenwerte von Integralgleichungen. Math. Z.47, 395–398 (1942).Google Scholar
- 3.——: Einschließungssätze für die charakteristische Zahlen von Matrizen. Math. Z.48, 221–226 (1942/43)Google Scholar
- 4.Hadeler, K. P.: Eigenwerte von Operator-Polynomen. Arch. Rational Mech. Anal.20, 72–80 (1965)Google Scholar
- 5.—: Einschließungssätze bei normalen und bei positiven Operatoren. Arch. Rational Mech. Anal.21, 58–88 (1966).Google Scholar
- 6.Hall, C. A., Spanier, J.: Nested bounds for the spectral radius. SIAM J. Numer. Anal.5, 113–125 (1968).Google Scholar
- 7.Krasnosel'skii, M. A.: Positive solutions of operator equations. Gos. Izd. Techn. Lit. Moscow, 1962 (Russian).Google Scholar
- 8.Krein, M. G., Rutman, M. A.: Linear operators leaving a cone invariant in a Banach space. Uspekhi Mat. Nauk. III, Nl, 3–95 (1948) (Russian).Google Scholar
- 9.Kulisch, U.: Über reguläre Zerlegungen von Matrizen und einige Anwendungen. Numer. Math.11, 444–449 (1968).Google Scholar
- 10.Marek, I.: Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iterations. Czechoslovak Math. J.12, 536–554 (1962).Google Scholar
- 11.: On the approximative construction of the eigenvectors corresponding to a pair of complex conjugated eigenvalues. Mat.-Fyz. Časopis Sloven. Akad. Vied.14, 477–488 (1964).Google Scholar
- 12.——: On the approximate construction of the spectral radius of a positive irreducible operator. Apl. Mat.12, 351–363 (1967) (Czech.).Google Scholar
- 13.——: On the polynomial eigenvalue problem with positive operators and the location of the spectral radius. Apl. Math.14, 146–159 (1969)Google Scholar
- 14.——: Spektrale Eigenschaften der K-positiven Operatoren und Einschließungssätze für den Spektralradius. Czechoslovak Math. J.16, 493–517 (1966).Google Scholar
- 15.——: Über einen speziellen Typus der linearen Gleichungen im Hilbertschen Raume. Časopis Pěst. Mat.89, 155–172 (1964).Google Scholar
- 16.Niiro, F., Sawashima, I.: On the spectral properties of positive irreducible operators in an arbitrary Banach lattice and problems of H. H. Schaefer. Sci. Papers College Gen. Ed. Univ. Tokyo16, 145–183 (1966).Google Scholar
- 17.Sawashima, I.: On spectral properties of some positive operators. Natur. Sci. Rep. Ochanomizu Univ.15, 55–64 (1964).Google Scholar
- 18.Schaefer, H.: Halbgeordnete lokalkonvexe Vektorräume. Math. Ann.135, 115–141 (1958).Google Scholar
- 19.——: Halbgeordnete lokalkonvexe Vektorräume. II. Math. Ann.138, 254–286 (1959)Google Scholar
- 20.——: On the singularities of an analytic function with values in Banach space. Arch. Math.11, 40–43 (1960).Google Scholar
- 21.——: Spectral properties of positive linear transformations. Pacific J. Math.10, 1009–1019 (1960).Google Scholar
- 22.Taylor, A. E.: Introduction to functional analysis. New York: J. Wiley 1958.Google Scholar
- 23.Varga, R. S.: Matrix iterative analysis. Englewood Cliffs, New Jersey: Prentice-Hall Inc. 1962.Google Scholar
- 24.Yamamoto, T.: A computational method for the dominant root of a nonnegative irreducible matrix. Numer. Math.8, 324–333 (1966).Google Scholar
Copyright information
© Springer-Verlag 1969