References
Bers, L., On mildly nonlinear partial difference equations of elliptic type. J. Res. Nat. Bur. Standards 51, 229–236 (1953).
Birkhoff, G., Lattice Theory. Am. Math. Soc. Colloquium Publ. V. XXV, Am. Math. Soc., 1948.
Collatz, L., Funktionalanalysis und Numerische Mathematik. Berlin-Göttingen-Heidel-berg: Springer 1964.
Ehrmann, H., Iterationsverfahren mit veränderlichen Operatoren. Arch. Rational Mech. Anal. 4, 45–64 (1959).
Gardner, G., Numerical Errors in Iterative Processes. Techn. Report, Division of Applied Mathematics, lBrown University, August 1965.
Kantorovich, L., The method of successive approximations for functional equations. Acta Math. 71, 63–97 (1939).
Kantorovich, L., B. Vulich, & A. Pinsker, Functional Analysis in Partially Ordered Spaces. Moscow: Gostechisdat 1950.
Nachbin, L., Topology and Order. Van Nostrand Math. Studies No.4. Princeton: Van Nostrand 1965.
Namioka, I., Partially ordered linear topological spaces. Mem. Am. Math. Soc. No.24, Am. Math. Soc., 1957.
Ostrowski, A., The rounding-off stability of iterations. Basel Math. Notes, BMN-12, August 20, 1964.
Rheinboldt, W., & J. Vandergraft, Partially-Ordered Topological Linear Spaces in Numerical Analysis (in preparation).
Schaefer, H., Topological Vector Spaces. New York: MacMillan 1966.
Schechter, S., Iteration methods for nonlinear problems. Trans. Amer. Math. Soc. 104, 179–189 (1962).
Schmidt, J., Konvergenzuntersuchungen und Fehlerabschätzungen für ein verallgemeinertes Iterationsverfahren. Arch. Rational Mech. Anal. 6, 261–276 (1960).
Schmidt, J., & H. Schönheinz, Fehlerschranken zum Differenzenverfahren unter ausschließlicher Benutzung verfügbarer Größen. Arch. Rational Mech. Anal. 10, 311–322 (1962).
Schröder, J., Das Iterationsverfahren bei verallgemeinertem Abstandsbegriff. Math. Z. 66, 111–116 (1956).
Toeplitz, O., Über lineare Mittelbildungen. Prace matem.-fizyczne 22, 113–119 (1911).
Urabe, M., Convergence of numerical iteration in solution of equations. Journal of Sci., Hiroshima Univ., A 19, 479–489 (1956).
Urabe, M., Error estimation in numerical solution of equations by iteration process. J. Sci., Hiroshima Univ. Ser. A-I 26, 77–91 (1962).
Vandergraft, J., On Newton's Method for Convex Operators on Partially Ordered Topological Linear Spaces. Univ. of Maryland, Comp. Sci. Center, Techn. Report TR-66-29, May 1966.
Varga, R., Matrix Iterative Analysis. Prentice Hall, Englewood Cliffs, N.J., 1962.
Warga, J., On a class of iterative procedures for solving normal systems of ordinary differential equations. J. Math. Phys. 31, 223–243 (1952).
Zincenko, O. I., A class of approximate methods for solving operator equations with non-differentiable operators. Dopovidi Akad. Nauk Ukrain RSR, No. 7, 852–856 (1963).
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Communicated by L. Collatz
This work was supported in part by NASA grant NsG-398 to the Computer Science Center and in part by the United States National Science Foundation grant PIVRO 6 to the Institute for Fluid Dynamics and Applied Mathematics at the University of Maryland.
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Ortega, J.M., Rheinboldt, W.C. On a class of approximate iterative processes. Arch. Rational Mech. Anal. 23, 352–365 (1967). https://doi.org/10.1007/BF00276778
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DOI: https://doi.org/10.1007/BF00276778