A note on the stability of the generalized Ritz method

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  • M. E. Titensky Ben-Gurion University of the Negev, Israel
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References

R.S. Anderssen and A.R. Mitchell, Analysis of generalized Galerkin methods in the numerical solution of eeliptic equations, Math. Meth. Appl. Sci., 1 (1979), pp. 3-15, https://doi.org/10.1002/mma.1670010102

D.S. Jones, Galerkin's method and stability, Math. Meth. Appl. Sci., 2 (1980), pp. 347-377, https://doi.org/10.1002/mma.1670020308

A.E. Martyniuk, Variational methods in boundary value problems for weakly elliptic equations, Dokl. Akad. Nauk SSSR, 126 (1959), pp. 1222-1225 (Russian).

A.E. Martyniuk, On the method's Galerkin-Krilov inverse variants, Vichislitenlnaya i prikladnaya mat., 14 (1971), pp. 18-35 (Russian).

S.G. Mikhlin, The numerical performance of variational methods, Wolters-Noordhoff Publishing, Groningen, 1971.

S.G. Mikhlin, Variational methods in mathematical physics, The Macmillan Co, New York, 1964.

S.G. Mikhlin, Errors of computational processes, Tbilis Gos. Univ., Tbilisi, 1983 (Russian).

S.G. Miklhlin, Some problems in error theory. Leningrad Univ., Leningrad, 1988 (Russian).

W.V. Petryshyn, Direct and iterative methods for the solution of linear operator equations in Hilbert space, Trans.Amer. Math. Soc., 105 (1962), pp. 136-175, https://doi.org/10.1090/s0002-9947-1962-0145651-8

W.V. Petryshyn, On a class of k-p.d. and non k-p.d. operators and operator equations, J. Math. Anal. Appl., 10 (1965), pp. 1-14, https://doi.org/10.1016/0022-247x(65)90142-3

W.V.Petryshyn, Projection methods in nonlinear numerical functional analysis, Journal of Math. and Mech., 17 (1967), pp. 353-372, https://doi.org/10.1512/iumj.1968.17.17019

M.E. Titensky, On the stability of the Galerkin method for certain coordinate systems, Izv. Vyssh. Uchebn. Zaved. Mat., 6 (1987), pp. 57-65 (Russian). Engish translation: Soviet Math (Iz VUZ) 31 (1987), no.6, pp. 73-82.

M. E. Titensky, On the stability of the Ritz method, The Institutue of scientific and Technical Informaiton, Moscow, on May 18, no.1782-79, (1979), 12 p. (Russian).

M. E. Titensky, On some suficient conditions of the stability of the Ritz and Bubnov-Galerkin methods, Ibid., on May 19, no.7924-80, (1980), 16 p. (Russian).

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Published

1994-08-01

How to Cite

Titensky, M. E. (1994). A note on the stability of the generalized Ritz method. Rev. Anal. Numér. Théor. Approx., 23(2), 217–225. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1994-vol23-no2-art10

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Vol. 23 No. 2 (1994)

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