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

MSC:
49J05Free problems in one independent variable (existence)
33C55Spherical harmonics
42C10Fourier series in special orthogonal functions
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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 · doi:10.1016/0016-0032(75)90199-4
[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.
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[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 · doi:10.1007/BF00927913
[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 · doi:10.1007/BF00935401
[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 · doi:10.1007/BF00932781
[13] Gradshteyn, I. S., andRyzhik, I. M.,Tables of Integrals, Series, and Products, Academic Press, New York, New York, 1977.