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For small scale problems, generalized inverses can be calculated easily by explicit matrix calculation during least squares optimization, or during SVD. However, for larger problems this becomes impractible. Several methods for approximation of the generalized inverse have been developed to circumvent this problem. In these methods no explicit matrix calculation is required. However, as the generalized inverse can not be solved explicitly, neither can the covariance matrix be provided by these methods. Several methods for obtaining the covariance matrix from the generalized inverse approximation are available. The approximation methods for the inverse and the covariance can be divided in two groups: iterative methods and model space weighting methods.
Both approaches are considered in this section.

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Stanford Exploration Project

9/18/2001