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Generalized nonlinear inverse problems solved using the least squares criterion
Author(s) -
Tarantola Albert,
Valette Bernard
Publication year - 1982
Publication title -
reviews of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.087
H-Index - 156
eISSN - 1944-9208
pISSN - 8755-1209
DOI - 10.1029/rg020i002p00219
Subject(s) - nonlinear system , inverse problem , mathematics , inverse , least squares function approximation , non linear least squares , variable (mathematics) , mathematical analysis , algorithm , estimation theory , physics , geometry , statistics , quantum mechanics , estimator
We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully nonlinear form. Second, we examine the general case where some data and/or unknowns may be functions of a continuous variable and where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodifferential equations). As particular cases of our nonlinear algorithm we find linear solutions well known in geophysics, like Jackson's (1979) solution for discrete problems or Backus and Gilbert's (1970) solution for continuous problems.