Summary
It is shown that the extended Kantorovich method introduced by Kerr [4] cannot be unconditionally stable. On the basis of this stability result, it is concluded that Kerr's claims for the extended Kantorovich method, though justified, are optimistic.
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Anderssen, R. S.: The numerical solution of parabolic differential equations using variational methods. Numer. Math.13, 129–145 (1969).
Branch, L.: Advanced calculus. New York: J. Wiley 1955.
Kantorovich, L. V., Krylov, V. L.: Approximate methods in higher analysis. Groningen: Noordhoff 1958.
Kerr, A. D.: An extension of the Kantorovich method. Quart. Appl. Math.26, 219–229 (1968).
—: An extended Kantorovich method for the solution of eigenvalue problems. Int. J. Solids Structures5, 559–572 (1969).
— Alexander, H.: An application of the extended Kantorovich method to the stress analysis of a clamped rectangular plate. Acta Mechanica6, 180–196 (1968).
Komkov, V.: An iterative method for obtaining decreasing sequences of upper bounds of functionals. Math. Res. Centre, Uni. of Wisconsin, Tech. Survey Report 534, November, 1964.
Mikhlin, S. G.: The problem of the minimum of a quadratic functional. San Francisco: Holden-Day, 1965.
—: The numerical performance of variational methods (Russian). Moscow: Nauka Publishers 1966. (To be published in English by Wolters-Noordhoff, Groningen, Jan., 1971).
Ostrowski, A. M.: Solution of equations and systems of equations. New York: Academic Press 1966.
Petryshyn, W.V.: On a class of a K-p.d. and non-K-p.d. operators and operator equations. J. Math. Anal. Appl.10, 1–24 (1965).
Schnuck, T. E.: Zur Knickfestigkeit schwach gekrümmter zylindrischer Schalen. Ingenieur Archiv4, 394–414 (1933).
Timoshenko, S., Goodier, J. N.: Theory of elasticity, Chapter II, second edition. New York: McGraw-Hill 1951.
Traub, J. F.: Iterative methods for the solution of equations. Prentice-Hall Series in Automatic Computation. Englewood Cliffs: Prentice-Hall 1964.
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Anderssen, R.S. A stability analysis for the extended Kantorovich method applied to the torsion problem. Numer. Math. 17, 239–246 (1971). https://doi.org/10.1007/BF01436380
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DOI: https://doi.org/10.1007/BF01436380