Abstract
A method is presented for locating a jump discontinuity in an otherwise-smooth function from its first few Fourier coefficients. It is based on a statistical model for otherwise-smooth functions and Bayes estimation, similar to and based on the work in [3]. Numerical results are presented, showing respectable performance, and comparing it to the jump locating algorithm of [1].
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References
Gelb, A., Tadmor, E.: Detection Of Edges in Spectral Data. Applied And Computational Harmonic Analysis 7, 101–135 (1999)
Gelb, A., Tadmor, E.: Detection Of Edges in Spectral Data II. Nonlinear Enhancement. SIAM J. Numer. Anal. 38, 1389–1408 (2000)
Solomonoff, A.: Reconstruction of a Discontinuous Function From a Few Fourier Coefficients Using Bayesian Estimation. J. Sci. Comput. 10(1) (1995)
Golub, G.H., Van Loan, C.F.: Matrix Computations, 2nd edn. Johns Hopkins University Press (1989)
Duda, R.O., Hart, P.E.: Pattern Classification And Scene Analysis. Wiley Interscience (1973)
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users’ Guide, 3rd edn. SIAM, Philadelphia (1999)
Galassi, M., et al.: GNU Scientific Library Reference Manual, revised 2nd edn., www.gnu.org/software/gsl/
Abramovitz, M., Stegun, I.A. (eds.): Handbook Of Mathematical Functions. Dover Publications (1964)
Boyd, J.P.: Chebyshev and Fourier Spectral Methods, revised 2nd edn. Dover Publications (2001)
Cover, T.M., Thomas, J.A.: Determinant Inequalities Via Information Theory. SIAM J. Matrix Anal. Appl. 9(3), 384–392 (1988)
Gottlieb, D., Shu, C.-W.: On the Gibbs Phenomenon IV: Recovering Exponential Accuracy in a Subinterval from a Gegenbauer Partial Sum of a Piecewise Analytic Function. Mathematics of Computation 64, 1081–1095 (1995)
Solomonoff, R.: The Application of Algorithmic Probability to Problems in Artificial Intelligence. In: Kochen, M., Hastings, H.M. (eds.) Advances in Cognitive Science. AAAS Selected Symposium Series, pp. 210–227 (1988)
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Solomonoff, A. (2013). Locating a Discontinuity in a Piecewise-Smooth Periodic Function Using Bayes Estimation. In: Dowe, D.L. (eds) Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence. Lecture Notes in Computer Science, vol 7070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-44958-1_28
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DOI: https://doi.org/10.1007/978-3-642-44958-1_28
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