Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
U. Ascher, Discrete least squares approximations for ordinary differential equations, MRC Technical Summary Report #1654 (1976).
R. Bellman, A note on an inequality of E. Schmidt, Bull. Amer. Math. Soc., 50 (1944), pp. 734–736.
J. H. Bramble and A. H. Schatz, Least squares methods for 2mth order elliptic boundary-value problems, Math. Comput., 25(1971), pp. 1–32.
P. J. Davis, Interpolation and Approximation, Dover Publications, New York, 1975.
C. DeBoor and B. Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal., 10 (1973), pp. 582–606.
J. Douglas, Jr., and T. Dupont, Galerkin approximations for the two-point boundary problem using continuous, piecewise polynomial spaces, Numer. Math., 22 (1974), pp. 99–109.
J. Douglas, Jr., T. Dupont, and L. Wahlbin, Optimal L∞ error estimates for Galerkin approximations to solutions of two-point boundary value problems, Math. Comput., 29 (1975), pp. 475–483.
N. Dunford and J. T. Schwartz, Linear Operators. I, II, Pure and Appl. Math., vol. 7, Interscience, New York, 1958, 1963.
R. Kannan and J. Locker, Nonlinear boundary value problems and operators TT*, J. Differential Equations, to appear.
E. B. Karpilovskaya, A method of collocation for integro-differential equations with biharmonic principal part, U.S.S.R. Computational Math. and Math. Phys., 10 (1970), pp. 240–260.
J. Locker, The generalized Green's function for an nth order linear differential operator, Trans. Amer. Math. Soc., to appear.
J. Locker and P. M. Prenter, Optimal L2 and L∞ error estimates for continuous and discrete least squares methods for boundary value problems, to appear.
P. M. Prenter, Splines and Variational Methods, John Wiley & Sons, New York, 1975.
P. M. Prenter and R. D. Russell, Orthogonal collocation for elliptic partial differential equations, SIAM J. Numer. Anal., 13 (1976), to appear.
P. A. Raviart, The use of numerical integration in finite element methods for solving parabolic equations, Topics in Numerical Analysis (Proc. Roy. Irish Acad. Conf., Dublin, 1972), J. Miller, ed., Academic Press, London, 1973, pp. 233–264.
R. D. Russell and L. F. Shampine, A collocation method for boundary value problems, Numer. Math., 19 (1972), pp. 1–28.
R. D. Russell and J. M. Varah, A comparison of global methods for linear two-point boundary value problems, Math. Comput., 29(1975), pp. 1–13.
P. Sammon, The discrete least squares method, Master's Thesis University of British Columbia. See also: The discrete least squares method, Math. Comput., 31 (1977), pp. 60–65.
B. K. Swartz and R. S. Varga, Error bounds for spline and L-spline interpolation, J. Approx. Theory, 6 (1972), pp. 6–49.
J. Todd (ed.), A Survey of Numerical Analysis, McGraw-Hill, New York, 1962.
G. Vainikko, The convergence of the collocation method for non-linear differential equations, U.S.S.R. Computational Math. and Math. Phys., 6 (1966), pp. 35–42.
M. F. Wheeler, An optimal L∞ error estimate for Galerkin approximations to solutions of two-point boundary value problems, SIAM J. Numer. Anal., 10 (1973), pp. 914–917.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Locker, J., Prenter, P.M. (1979). On least squares methods for linear two-point boundary value problems. In: Nashed, M.Z. (eds) Functional Analysis Methods in Numerical Analysis. Lecture Notes in Mathematics, vol 701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062079
Download citation
DOI: https://doi.org/10.1007/BFb0062079
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09110-3
Online ISBN: 978-3-540-35530-4
eBook Packages: Springer Book Archive