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Chang, R. Y.; Wang, M. W.

Shifted Legendre direct method for variational problems. (English) Zbl 0481.49004

J. Optimization Theory Appl. 39, 299-307 (1983).
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Cited in 65 Documents

MSC:

49J05 Existence theories for free problems in one independent variable
33C55 Spherical harmonics
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Keywords:

shifted Legendre polynomials; operational matrix
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\textit{R. Y. Chang} and \textit{M. W. Wang}, J. Optim. Theory Appl. 39, 299--307 (1983; Zbl 0481.49004)
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References:

[1] Schechter, R. S.,The Variational Method in Engineering, McGraw-Hill Book Company, New York, New York, 1967. · Zbl 0176.10001
[2] Chen, C. F., andHsiao, C. H.,A Walsh Series Direct Method for Solving Variational Problems, Journal of Franklin Institute, Vol. 300, No. 4, pp. 265-280, 1975. · Zbl 0339.49017
[3] Villadsen, J., andMichelsen, M. L.,Solution of Differential Equation Models by Polynomial Approximation, Prentice-Hall, Englewood Cliffs, New Jersey, 1978. · Zbl 0464.34001
[4] Ross, B., andFarrell, O. J.,Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions, The Macmillan Company, New York, New York, 1963.
[5] Hwang, C.,Study of Operational Matrix Method in Dynamic Systems, National Cheng Kung University, Department of Chemical Engineering, PhD Thesis, 1981.
[6] Chen, W. L.,Application of Walsh Functions to Time-Varying and Delay Systems, National Cheng Kung University, Department of Electrical Engineering, PhD Thesis, 1977.
[7] Hwang, C., andShih, Y. P.,Laguerre Series Direct Method for Variational Problems, Journal of Optimization Theory and Applications, Vol. 39, No. 1, pp. 143-149, 1983. · Zbl 0481.49005
[8] Kelley, H. J.,Gradient Theory of Optimal Flight Paths, AIAA Journal, Vol. 30, No. 10, pp. 947-954, 1960. · Zbl 0096.42002
[9] Bryson, A. E., Jr., andDenham, W. F.,A Steepest-Ascent Method for Solving Optimum Programming Problems, Journal of Applied Mechanics, Vol. 84, No. 3, pp. 247-257, 1962. · Zbl 0112.20003
[10] Miele, A., Pritchard, R. E., andDamoulakis, J. N.,Sequential Gradient Restoration Algorithm for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 5, No. 4, pp. 235-282, 1970. · Zbl 0192.51802
[11] Miele, A., Tietze, J. L., andLevy, A. V.,Summary and Comparison of Gradient-Restoration Algorithms for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 10, No. 6, pp. 381-403, 1972. · Zbl 0233.49009
[12] Miele, A.,Recent Advances in Gradient Algorithms for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 17, Nos. 5/6, pp. 361-430, 1975. · Zbl 0296.49024
[13] Gradshteyn, I. S., andRyzhik, I. M.,Tables of Integrals, Series, and Products, Academic Press, New York, New York, 1977.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.