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Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip. (German) Zbl 0291.65017


MSC:

65J05 General theory of numerical analysis in abstract spaces
65H10 Numerical computation of solutions to systems of equations
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References:

[1] W. Burmeister, Inversionsfreie Verfahren zur Lösung nicht linearer Operatorgleichungen,Z. Angew. Math. Mech. 52 (1972), 101–110. · Zbl 0291.65015 · doi:10.1002/zamm.19720520205
[2] W. Hofmann,Regula-falsi-Verfahren in Banachräumen, Diss. Univ. Hamburg, 1970.
[3] J. M. Ortega, The Newton–Kantorovich theorem,Amer. Math. Monthly 75 (1968), 658–660. · Zbl 0183.43004 · doi:10.2307/2313800
[4] W. C. Rheinboldt, A unified convergence theory for a class of iterative processes,SIAM J. Numer. Anal. 5 (1968), 42–63. · Zbl 0155.46701 · doi:10.1137/0705003
[5] J. M. Ortega andW. C. Rheinboldt,Iterative solution of nonlinear equations in several variables, New York-London, 1970. · Zbl 0241.65046
[6] J. W. Schmidt, Eine Übertragung der Regula falsi auf Gleichungen in Banachräumen,Z. Angew. Math. Mech. 43 (1963), 1–8 und 97–110. · Zbl 0115.34002 · doi:10.1002/zamm.19630430102
[7] S. Ulm, Das Majorantenprinzip und die Sehnenmethode,Izv. Akad. Nauk Eston. SSR 13 (1964), 217–227 (in Russian).
[8] J. E. Dennis, Toward a unified convergence theory for Newton-like methods,Nonlinear Functional Analysis and Applications, New York-London, 1971, 425–472.
[9] W. Hoyer, Das Majorantenprinzip bei Mehrschritt-Iterationsverfahren,Beiträge Numer. Math. 2 (1974), 39–60. · Zbl 0282.65043
[10] J. W. Schmidt, Überlinear konvergente Mehrschrittverfahren vom Regula falsi- und Newton-Typ,Z. Angew. Math. Mech. 53 (1973), 103–114 und54 (1974), 600. · Zbl 0288.65031 · doi:10.1002/zamm.19730530204
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