Numerical Recipes in FORTRAN—The Art of Scientific Computing 2nd Ed. (W. H. Press, W. T. Vetterling, S. A. Teukolsky and B. P. Flannery)

Yanik, Elizabeth Greenwell

doi:10.1137/1036047

Cited by 20 publications

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“…where x j is the j th singular value. The SVD method has an in-built measure of the standard deviation in the solution vector (Press et al 1992). If the standard deviation that is obtained from the singular value decomposition is included in the answer the solution vector can be written as…”

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“…This jump can be used to determine when a particular value of λ k is close to zero and hence to estimate the values of λ k that arise in the time series given by expression (25a). A more detailed discussion of the application of these ideas to analysing a noisy time series consisting of a superposition of decaying exponentials will be given elsewhere (Lawunmi 1997).…”

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A theoretical analysis of exponentially decaying time series

Lawunmi

1997

Meas. Sci. Technol.

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In this paper it is shown that it is sufficient to analyse a small region of an exponentially decaying signal in order to characterize it. A technique based on the singular value decomposition (SVD) method is developed to analyse time series consisting of an exponential function and a noisy background. Techniques for analysing time series that consist of more than one decaying exponential function are also discussed.

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confidence: 99%