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Model resolution estimate

Although the tridiagonal form found in (tridimat) is interesting in its own right, the more important result contained in (inverse4) is the fact that this analysis has resulted in a decomposition in terms of orthogonal (rather than merely conjugate) vectors. This result allows us to obtain the resolution matrix quickly for the model space from this form. In particular, if we define the diagonal matrix

D_G = G_n^TG_n,   we see that

M^TM G_nD_G^-1T_nD_G^-1 G_n^T,   and therefore, since

_model (M^TM)^ M^TM = M^TM(M^TM)^,   we find easily that

_model = G_nD_G^-1G_n^T = _i=1^n g_ig_i^T (g_i,g_i).  


previous up next print clean
Next: Data resolution estimate Up: RESOLUTION OPERATORS FOR BOTH Previous: Pseudoinverse estimate
Stanford Exploration Project
11/11/1997