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A Walsh series direct method for solving variational problems. (English) Zbl 0339.49017


MSC:

49M15 Newton-type methods
33E99 Other special functions
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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References:

[1] Rademacher, H., Einige Salze über Reihen von allgemeinen Orthogonafuntionen, Math. Ann., Vol. 87, 712-738 (1922)
[2] Walsh, J. L., A closed set of orthogonal functions, Am. J. Math., Vol. 45, 5-24 (1923)
[3] Lee, J. D., Review of recent work on applications of Walsh functions in communications, (Proc. Walsh Function Symp. (1970), Nav. Res. Labs: Nav. Res. Labs Wash. D.C), 26-35
[4] Harmuth, H. F., Application of Walsh function in communications, IEEE Spect., Vol. 6, No. 11, 82-91 (Nov. 1969)
[5] Gibbs, J. E.; Gebbie, H. A., Application of Walsh function to transform spectroscopy, Nature, Vol. 224, 1012-1013 (Dec. 1969)
[6] Thomas, C. W.; Welch, A. J., Heart rate representation using Walsh functions, (Proc. Walsh Function Symp. (1972), Nav. Res. Labs: Nav. Res. Labs Wash., D.C), 154-158
[7] Picher, F., Walsh function and optimal linear systems, (Proc. Walsh Function Symp. (1970), Nav. Res. Labs: Nav. Res. Labs Wash., D.C), 17-22
[8] Corrington, M. S., Solution of differential and integral equations with Walsh functions, IEEE Trans. Circuit Theory, Vol. CT-20, No. 5, 470-475 (Sept. 1973)
[9] Gelfand, I. M.; Fomin, S. V., Calculus of Variations (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0127.05402
[10] Brewster, C. D., Approximate Methods of Higher Analysis (1958), Interscience: Interscience New York · Zbl 0083.35301
[11] Elsgolc, E. L., Calculus of Variation (1961), Pergamon Press: Pergamon Press London · Zbl 0101.32001
[12] Schechter, R. S., The Variation Method in Engineering, ((1967), McGraw-Hill: McGraw-Hill New York), 23-24 · Zbl 0176.10001
[13] Neuman, C. P.; Sen, A., Weighted residual methods in optimal control, IEEE Trans. Auto Control, Vol. AC-19, 67-69 (Feb. 1974) · Zbl 0291.49026
[14] Mang, J. H., A sequency-ordered fast Walsh transform, IEEE Trans. Audio X Electroacoust, Vol. AU-20, No. 3, 204-205 (1972)
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