In order to save computational resources, a non-iterative algorithm based on both Horowitz-Sahni scheme (to manage sparse matrix) and the Ohio State University (OSU) algorithm (to compute matrix inversion) is proposed. The algorithm deals with least-squares solution characteristics, by structuring data for speeding up access. It is applied to the unsymmetric rectangular system matrix, which compaction improves both time and memory requirements up to 98% for only the matrix. Afterwards, symmetrical matrices are compressed and the OSU algorithm is modified in order to save additional demand in about 50%. In all cases, removal of redundant elements yields a significative reduction in access, and consequently, in the overall time and memory requirements. The algorithm was tested in a 2,000 Rayleigh wave paths dataset for various grid cell sizes, and the results were compared with both full storage and Singular Value Decomposition (SVD) techniques. Those tests showed that the economy varies from 65% to 98%. It was also applied in two real cases in Southeastern and Northeastern Brazil, using a standalone Personal Computer (PC), which demand was reduced by a factor of sixteen, with no loss of accuracy. Although the algorithm is intended to a specific problem in Seismology (surface wave tomography), it also allows to whichever is the sparse system solution, including the rigorous computation of resolution and covariance matrices.
Group-velocity tomography; Damped least-squares; Sparse system; Full resolution and covariance matrices; Speeding up processing
