Abstract
The inversion of potential field data has widely utilized the generalized cross-validation (GCV) and the unbiased predictive risk estimator (UPRE) methods to determine the regularization parameter. However, these two methods are time-consuming and it is difficult for them to determine the optimal linear search range including the optimal regularization. To solve these problems, this article improves the GCV and UPRE methods using the RGSVD (randomized generalized singular value decomposition) algorithm. The improved methods first use the randomized algorithm to compute an approximate generalized singular value decomposition (GSVD) with less computational time. Then, the optimal linear search range is determined based on the generalized singular values. Finally, the GCV and the UPRE functions are efficiently computed on the basis of the results from the RGSVD algorithm. In this way, the GCV and UPRE methods using the RGSVD algorithm are able to determine the optimal regularization parameter fast and effectively. One comparative test shows the effectiveness and efficiency of the GCV and the UPRE methods using the RGSVD algorithm.
Highlights
When using the generalized singular value decomposition (GSVD), the optimal linear search range can be determined by analyzing the spectrum of the kernel matrix [9], but computational costs and memory requirements limit the application of this method
The Randomized generalized singular value decomposition (RGSVD) algorithm uses a randomized algorithm to compute an approximation of the GSVD with less memory requirements and computing time [10], with which the optimal linear search range can be determined based on the generalized singular values
One comparative test demonstrated the performances of the generalized cross-validation (GCV) and the unbiased predictive risk estimator (UPRE) methods using the RGSVD algorithm
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Method and generalized singular value decomposition (GSVD) can be used to compute the GCV and the UPRE functions in a linear search range to find the optimal regularization parameter. When using the GSVD, the optimal linear search range can be determined by analyzing the spectrum (generalized singular values) of the kernel matrix [9], but computational costs and memory requirements limit the application of this method. The RGSVD [10] algorithm was adopted in the GCV and the UPRE methods for determination of the optimal regularization parameter. The RGSVD algorithm uses a randomized algorithm to compute an approximation of the GSVD with less memory requirements and computing time [10], with which the optimal linear search range can be determined based on the generalized singular values. One comparative test demonstrated the performances of the GCV and the UPRE methods using the RGSVD algorithm
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