1. Well-posed and ill-posed inverse problems and diagnostic tools
1.1 Hadamard's conditions
Let x be the vector of unknown parameters to be identified ( x ΠX and y mo the modeled vector ( y mo ΠY.
We're talking about finite dimensions here, and X and Y are two normed vector spaces.
Consider an operator H;;, linear or not, representing the model and applying X in Y. We then have y mo = H x and both the model and the direct problem (finding y mo knowing ;;x) are shown in figure 1 a.
Inversion consists in...
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Well-posed and ill-posed inverse problems and diagnostic tools
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