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Least squares approximations for dual trigonometric series

Published online by Cambridge University Press:  18 May 2009

Robert B. Kelman  and
Chester A. Koper Jr
Robert B. Kelman
Affiliation:
Colorado State University, Fort Collins, Colorado 80521, U.S.A.
Chester A. Koper Jr
Affiliation:
Colorado State University, Fort Collins, Colorado 80521, U.S.A.
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A systematic and easily automated least squares procedure, not using integral equations or special functions, is presented for approximating the solutions of general dual trigonometric equations. This is desirable, since current analytic methods apply only to special equations, require the use of integral equation and special function theory, and do not lend themselves easily to numerical work; see, e.g. [1, 2, 6, 8, 9,10, 11, 12, 13, 14, 15, 16, 17].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 111 - 119
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Cooke, J. C., Note on a pair of dual trigonometric series, Glasgow Math. J. 9 (1968), 30–35.CrossRefGoogle Scholar
2.Cooke, J. C., The solution of some integral equations and their connections with dual integral equations and series, Glasgow Math. J. 11 (1970), 9–20.CrossRefGoogle Scholar
3.Davis, P. J. and Rabinowitz, P., Numerical integration (Waltham, Massachusetts, 1967).Google Scholar
4.Ince, E. L., Ordinary differential equations (New York, 1956).Google Scholar
5.Klyuyev, V. V. and Kokovkin-Shcherbak, N. I., On the minimization of the number of arithmetic operations for the solution of linear algebraic systems of equations, Vyčsl. Mat. i Mat. Fiz. 5 (1965), 21–33.Google Scholar
6.Kudriavtsev, B. A. and Parton, V. Z., Dual trigonometric series in crack and punch problems, Prikl. Mat. Meh. 33 (1969), 844–849.Google Scholar
7.Lanczos, C., Discourse on Fourier series (New York, 1966).Google Scholar
8.Noble, B. and Hussain, M. A., Exact solution of certain dual series for indentation and inclusion problems, Int. J. Eng. Sci. 7 (1969), 1149–1161.CrossRefGoogle Scholar
9.Noble, B. and Whiteman, J. R., Solution of dual trigonometrical series using orthogonality relations, SI AMJ. Appl. Math 18 (1970), 372–379.CrossRefGoogle Scholar
10.Noble, B. and Whiteman, J. R., The solution of dual cosine series by the use of orthogonality relations, Proc. Edinburgh Math. Soc. 17 (1970), 47–51.CrossRefGoogle Scholar
11.Sneddon, I. N., Mixed boundary value problems in potential theory (Amsterdam, 1966).Google Scholar
12.Srivastav, R. P., Dual series relations III. Dual relation involving trigonometric series, Proc. Roy. Soc. Edinburgh, Sect. A, 66 (1964), 173–209.Google Scholar
13.Tranter, C. J., Dual trigonometric series, Proc. Glasgow Math. Assoc. 4 (1959), 49–57.CrossRefGoogle Scholar
14.Tranter, C. J., A further note on dual trigonometric series, Proc. Glasgow Math. Assoc. 4 (1960), 198–200.CrossRefGoogle Scholar
15.Tranter, C. J., An improved method for dual trigonometric series, Proc. Glasgow Math. Assoc. 6 (1964), 136–140.CrossRefGoogle Scholar
16.Whiteman, J. R., Treatment of singularities in a harmonic mixed boundary value problem by dual series methods, Quart. J. Mech. Appl. Math. 21 (1968), 41–50.CrossRefGoogle Scholar
17.Williams, W. E., The solution of dual series and dual integral equations, Proc. Glasgow Math. Assoc. 6 (1964), 123–129.CrossRefGoogle Scholar