In the process of solving inverse gaphysical problems, the conjugate gradient (CG) method is one of the classical and valuable main algorithms. Based on classical conjugate gradient standard algorithm, the present paper made further development and deduced the standard algorithm forms for figuring out damping(IRLS)solution under the meaning of least absolute deviation(LAD), which resulted in more generalization of the application of the CG method. This method is called generalized conjugate gradient (GCG) method.In order to render the functions of GCG method more understandable. the paper has given two examples and compared the calculations with the calculations obtained by the generally recognized singular value decompeition(SVD)algorithm for figuring out morbid problems. The results show that the GCG method is characterized by strong capacity for solving morbid problems, high precision and fast operation speed. In addition, the GCG method obviously has two more features:(1) simple algorithm and flexible programming; (2) the capacity for maintaining spare characteristics of the coefficient matrix.
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