Geodesic
Numerical evaluation of the truncated singular value decomposition within the seismic traveltimes tomography framework
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 2, pp. 224-234

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The method of truncated singular value decomposition is a powerful tool of regularization and solution of inverse problems. Application of this method is limited by the memory requirements for the calculation of singular value decomposition of matrices. The solution is a usage of iterative procedures, that provide the possibility to evaluate only the largest singular values and corresponding vectors. For the practical application of this methodology one should answer the questions: what part of the spectrum can be determined numerically and whether the number of singular vectors is enough for the solution. These problems are considered in the present paper within the seismic traveltimes inversion framework.
Keywords: inverse problems, numerical methods, truncated singular value decomposition, geophysics, seismic traveltimes. 
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Alexandr S. Serdyukov; Andrey V. Patutin; Tatiana V. Shilova. Numerical evaluation of the truncated singular value decomposition within the seismic traveltimes tomography framework. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 2, pp. 224-234. http://geodesic.mathdoc.fr/item/JSFU_2014_7_2_a9/