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Untere Fehlerschranken für Regula-Falsi-Verfahren. (German) Zbl 0401.65036

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
Full Text: DOI
[1] G. Alefeld, An exclusion theorem for the solutions of operator equations,Beiträge Numer. Math. 6 (1977), 7–10. · Zbl 0365.65039
[2] W. Burmeister, Inversionsfreie Verfahren zur Lösung nichtlinearer Operatorgleichungen,Z. Angew. Math. Mech. 52 (1972), 101–110.MR 45#9213 · Zbl 0291.65015 · doi:10.1002/zamm.19720520205
[3] J. E. Dennis, Toward a unified convergence theory for Newton-like methods,Nonlinear Functional Anal. and Appl. (Proc. Sem. Madison, Wis., 1970), Academic Press, 1971, 425–472.MR 43#4286
[4] W. B. Gragg andR. A. Tapia, Optimal error bounds for the Newton-Kantorovich theorem,SIAM J. Numer. Anal. 11 (1974), 10–13.MR 49#8334 · Zbl 0284.65042 · doi:10.1137/0711002
[5] W. Hofmann, Regula-falsi-Verfahren in Banachräumen, Diss. Univ. Hamburg, 1970.
[6] W. Hofmann, Konvergenzsätze für Regula-falsi-Verfahren,Arch. Rational Mech. Anal. 44 (1971–72), 296–309.MR 49#8324. · Zbl 0236.65037
[7] W. Hoyer, Das Majorantenprinzip bei Mehrschritt-Iterationsverfahren,Beiträge Number. Math. 2 (1974), 39–60. · Zbl 0282.65043
[8] J. W. Schmidt, Eine Übertragung der Regula falsi auf Gleichungen in Banachräumen I,Z. Angew. Math. Mech. 43 (1963), 1–8.MR 26#5442 · Zbl 0115.34002 · doi:10.1002/zamm.19630430102
[9] J. W. Schmidt, Eine Übertragung der Regula falsi auf Gleichungen in Banachräumen II,Z. Angew. Math. Mech. 43 (1963), 97–110.MR 27#616 · Zbl 0115.34002 · doi:10.1002/zamm.19630430302
[10] J. W. Schmidt, Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip,Period. Math. Hungar. 5 (1974), 187–193.MR 50#8957 · Zbl 0291.65017 · doi:10.1007/BF02023198
[11] S. Ulm, Princip mažorant i metod hord (A majorant principle and the method of secants),Eesti NSV Tead. Akad. Toimetised Füüs.-Math. Techn.-tead. Seer 13 (1964), 217–227. (In Russian; Estonian and English summaries)MR 29#5369
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