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R. Parker (1972)
Inverse Theory with Grossly Inadequate DataGeophysical Journal International, 29
Sabatier Sabatier (1977)
Positivity constraints in linear inverse problemsGeophys. J. Roy. Astron. Soc., 48
P. Sabatier (1977)
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R. Parker (1977)
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Calyampudi Rao (1965)
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F. Gilbert, A. Dziewoński (1975)
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R. Parker (1971)
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Backus (1970)
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George Backus (1970)
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G. Backus, F. Gilbert (1970)
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Parker Parker (1975)
The theory of ideal bodies for gravity interpretationGeophys. J. Roy. Astron. Soc., 42
Backus (1970)
Inference from inadequate and inaccurate data, IProc. Nat. Acad. Sci. U.S., 65
R. Wiggins (1972)
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The algebraic eigenvalue problem
A version of Backus's theory of linear inference is developed by using a new finite‐dimensional space. This approach affords a clear geometric interpretation of the essential role played by a priori model smoothing assumptions and also facilitates the construction of a theory for the treatment of random data errors that is quite different from the treatment of Backus. When the unknown parameters form a (necessarily incomplete) description of the model, it is possible to formulate a special smoothing assumption that is particularly appropriate; in practical examples this strategy often leads to tighter bounds on the model uncertainty than those obtained with previous assumptions. An analysis of the numerical aspects of the problem forces one to the conclusion that the theory is not competitive numerically with conventional least squares parameter estimation, unless one of the large submatrices in the problem possesses a simple inverse. An example of this kind is discussed briefly.
Reviews of Geophysics – Wiley
Published: Nov 1, 1977
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