Saturation theorems for Bernstein polynomials in Banach subspaces of

Grundmann, Axel

doi:10.1016/0021-9045(79)90010-8

Cited by 7 publications

(1 citation statement)

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“…Such transforms are said to have the property of positivity (Lorentz 1953;Karlin 1968;Karlin and Ziegler 1970). Such transforms are also known to be variation-diminishing and there is a growing amount of literature (Lorentz 1953;Hirschman and Widder 1955;Karlin 1968;Karlin and Karon 1968;Jones 1976;Schurer and Steutel 1977;Porter 1978;Grundmann 1979;Ramakrishna 1978;Ramakrishna et al 1979;Nagel 1980;Wood 1984;Derriennic 1985) on them. The Backus-Gilbert formalism is expected to gain by drawing from it.…”

Section: (66)mentioning

confidence: 99%

Inversion of potential field data

Moharir

1990

Proc. Indian Acad. Sci. (Earth Planet Sci.)

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The problem of inversion of potential field data is a challenging one because of the diftieulty in obtaining a unique solution. This paper identifies various types of nonuniqueness and argues that it is neither possible nor necessary to remove all categories of nonuniqueness. Some types of nonuniqueness are due to human limitations and choice and these would always persist.Listing all the solutions, imposing additional constraints on the acceptable solutions, a priori idealization, use of a priori or supplementary information, characterizing what is common to all the solutions, obtaining extremal solutions, seeking a distribution of all possible solutions, etc. are various responses in the face of nonuniqueness. It is shown that merely the form of nonuniqueness is changed by all these techniques. Some algorithms, which should be used to obtain the global minimum of the objective function are discussed.The conceptual commonality underlying seemingly different approaches and the possibility of nonunique interpretations of the same numerical results due to different axiomatic contexts are both elucidated.

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