Author | Britton, Wray. author |
---|---|
Title | Conjugate Duality and the Exponential Fourier Spectrum [electronic resource] / by Wray Britton |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5528-4 |
Descript | VIII, 226 p. online resource |
1. Introduction -- 2. Imposing the constraints -- 3. Selecting the objective functional: conjugate duality -- 4. Choosing a truncation point for (c*c)k -- 5. Solving for Solving for $$\vec{\theta}{\rm̂{(n)}: n=1}$$ -- 6. Solving for $$\vec{\theta}{\rm̂{(n)}: n > 1}$$ -- 7. Obtaining an initial estimate $$\hat{\vec{\theta}}̂{(\rm n)}$$ of $$\vec{\theta}̂{(\rm n)}$$ -- 8. Numerical asymptotics -- 9. Assessing the sample efficiency of $$\hat{\vec{\rm b}}̂{(\rm n)}$$ and $$\hat{\vec{\theta}}̂{(\rm n)}$$ -- 10. The numerical experiment: preliminaries -- 11. The numerical experiment: results -- 12. Tables and graphs -- Fig. 1 The Sunspot Cycle: 1610โ1976 -- Fig. 2 The Autocorrelogram of the untransformed data -- Fig. 3 The Autocorrelogram of the transformed data -- Table 1 Summary analysis for fn* -- Table 2 Summary analysis for fn -- Table 3 Order determination of fn* on the Akaike (1977) criterion -- Table 4 Summary analysis of fn* -- Table 5 Asymptotic analysis of Zn (11 ? n ? 20) -- Figs. 4โ23 Simultaneous plot of fn* (k = 1) -- 13. Conclusion -- Appendix A: Comparison of Steffensen(1), simplified N-R(2), unmodified N-R(3), and Laguerre(4) update strategies for solving A(x) = r for x given r = 0(0.01)0.93 -- Appendix C: ANSI โ77 FORTRAN source code listing (MAIN) -- Appendix D: ANSI โ77 FORTRAN source code listing (FOLLOW-UP) -- Appendix H: ANSI โ77 FORTRAN source code (Korovkin)