By G. Wahba (auth.), Andreas Vogel, Charles O. Ofoegbu, Rudolf Gorenflo, Bjorn Ursin (eds.)
Read or Download Geophysical Data Inversion Methods and Applications: Proceedings of the 7th International Mathematical Geophysics Seminar held at the Free University of Berlin, February 8–11, 1989 PDF
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Additional info for Geophysical Data Inversion Methods and Applications: Proceedings of the 7th International Mathematical Geophysics Seminar held at the Free University of Berlin, February 8–11, 1989
M. Mikhail/F. Ackermann (1976, p. 341). 7a,b) the "natural iterative inhornBLIP". Unfortunately, this scheme turns out to be unstable because of the matrix ATA + Pk1Im which is to be inverted in spite of becoming more and more ill-conditioned for large indices k. V. J. G. w. T. King/ D. Chillingworth (1979) and, in particular, E. Schock (1984; 1987) who gave it the name "Fakeev-Lardy iteration". 13b) which - surprisingly enough - generates a stable scheme due to the fact that always the same matrix ATA + p-1Im is to be inverted for a suitably chosen "variance ratio" p > O.
Thus the question arises as to how we can robustify the method of "conjugate gradients" when simultaneously accelerating the convergence. However, this investigation will be postponed to future research. 6. , 1972: Regression and the Moore-Penrose Pseudoinverse. Academic Press, New York. W. W. ), Inverse and Ill-Posed Problems. Academic Press, Boston, 165-175. Brill, M. and E. Schock, 1987: Iterative solution of ill-posed problems a survey; in: A. ), Model Optimization in Exploration Geophysics.
Ions. ed by N, let. m ... he set. s of problem (24) and "l¢(;;') ... v k ( c;;' + + p) k ~ w~ a. he gradient. v ) at. he point. x. he columns of N are linearly independent. g. see Goldfarb-Idnani(1983» N* .. ( NT C- 1 N ) -1NT C-1 (25a) a-1~I (25b) H ... 1/vk ... he - - NN*) ... ions (26) It. ant. hat. s xkem. h unique multipliers u. ep 2 we have Jk .. ion ¢(x,wk,v k ). ion is given by Ak X The direct. ions 26 .. ions which at. 2: w. y. hat. 01 has q columns. g. rb-Idnani(1983». TJk(. k. riangulal' , given, these if' a i'easible calculations solution can be x k f'or pert'ormed easily.
Geophysical Data Inversion Methods and Applications: Proceedings of the 7th International Mathematical Geophysics Seminar held at the Free University of Berlin, February 8–11, 1989 by G. Wahba (auth.), Andreas Vogel, Charles O. Ofoegbu, Rudolf Gorenflo, Bjorn Ursin (eds.)