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Sonderdruck aus "Numerische Mathematik" 20, 312-316 (1973)
 

Summary: Sonderdruck aus
"Numerische Mathematik" 20, 312-316 (1973)
(Q by Springer- Verlag 1973
Prinled in Germany
Über Konvergente Zerlegungen von Matrizen
G. ALE FELD
Herrn Professor Dr. Johannes Weissinger
zum 60. Geburtstag gewidmet
Numer. Math. 20, 312-316 (1973)
«d by Springer-Verlag 1973
Über konvergente Zerlegungen von Matrizen
G. Alefeld
Herrn Professor Dr. ]ohannes Weissinger zum 60. Geburtstag gewidmet
Eingegangen am 14. April 1972
Abstract. Let A, M, N be n X n real matrices, let A = M - N, let A and M be
nonsingular. Let M'y 20 imply N'y >0 (where the prime denotes the transpose).
Then A' y > 0 implies N' y 20 if and only if the spectral radius e(M-l N) of M-l N is
less than one. This complements a result of Mangasarian, given in [1]. The same
conclusions are true if A', M', and N' are replaced by A, M, and N respectively. The
proof given here does not make use of the Perron-Frobenius theorem.

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics